Typed states for the displayed outbound observations.
Source: paper_references, paper_reference_links, observed 2026-08-04T06:19:02.268265Z
Paper Citation Record · LEDGER
As of 23 August 2026, this Paper Citation Record lists 95 of 95 outbound references and 0 inbound Pith citation observations for arXiv:2608.02494.
A citation records a reference. It does not transfer a finding from one paper to another.
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Source: paper_references, paper_reference_links, observed 2026-08-04T06:19:02.268265Z
One-hop event checks from named stored sources.
Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00
Pith citing papers itemized under the disclosed page cap.
Source: paper_references, paper_reference_links
A source-named dated measurement, never combined with another source.
Source: cited_works
95 of 95 outbound references displayed
External citation measurements
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Observation 6e61efdc-6a8b-4f0a-a79b-afe81160b1bf · outbound
Isogeny graphs of elliptic curves in characteristic zero Springer-Verlag, Berlin, 2001
Reference 1
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Observation 14e50aa6-5ec4-45fc-9c50-0da6308069f9 · outbound
Isogeny graphs of elliptic curves in characteristic zero Explicit connections between supersingular isogeny graphs and Bruhat-Tits trees
Reference 2
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Observation f1dbb23b-5338-4902-a580-1533b6326207 · outbound
Isogeny graphs of elliptic curves in characteristic zero Black box Galois representations.J
Reference 3
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Observation 17d6a3f3-30a6-4125-87ea-4d5d924dc859 · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 4
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Observation 2ae10e1e-7b58-463a-877f-ebd0d14d6e36 · outbound
Isogeny graphs of elliptic curves in characteristic zero Banwait and Maarten Derickx
Reference 5
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Observation bf868e70-12fb-47eb-a38c-ffc1871fcdd9 · outbound
Isogeny graphs of elliptic curves in characteristic zero Banwait, Filip Najman, and Oana Padurariu
Reference 6
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Observation 36782186-9f51-4a4b-9c5b-c2bb84301240 · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 7
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Observation 06017dcb-cd4e-43bf-a610-cd2ccbab7dc5 · outbound
Isogeny graphs of elliptic curves in characteristic zero Barrios, Maila Brucal-Hallare, Alyson Deines, Piper Harris, and Manami Roy
Reference 8
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Observation 0b1447a7-a3ca-45d3-bcfb-51c5c4747df3 · outbound
Isogeny graphs of elliptic curves in characteristic zero Barrios, Enrique Gonz´ alez-Jim´ enez, and Ivan Novak
Reference 9
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Observation 36feef7a-0e7f-444e-878d-eb31edb78cb4 · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 10
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Observation bcc782e0-321b-47ce-9af5-ecdf5f76a9f7 · outbound
Isogeny graphs of elliptic curves in characteristic zero The Magma algebra system
Reference 11
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Observation f7448620-7f3e-4cdd-a8f3-7e728fefa594 · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 12
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Observation f615de36-5523-4f85-b09e-ed59f1da9d6b · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 13
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Observation fefb9da6-56bf-4bab-9e78-c7f4b2b457b5 · outbound
Isogeny graphs of elliptic curves in characteristic zero Clark, and James Stankewicz
Reference 14
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Observation 7d4473e5-b5ef-4a22-9af9-78d742e64b26 · outbound
Isogeny graphs of elliptic curves in characteristic zero Sporadic points of odd degree on $X_1(N)$ coming from $\mathbb{Q}$-curves
Reference 15
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Observation 2978e73e-8f50-4658-b785-0a99959c5387 · outbound
Isogeny graphs of elliptic curves in characteristic zero Bruhat and J
Reference 16
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Observation d1ab1517-9cf5-4edd-8ba0-30ab538ec61d · outbound
Isogeny graphs of elliptic curves in characteristic zero Fields of definition of elliptic curves with prescribed torsion.Acta Arith., 181(1):85–95, 2017
Reference 17
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Observation a8294bac-36b1-4468-b776-46700203f03d · outbound
Isogeny graphs of elliptic curves in characteristic zero Essays in harmonic analysis on p-adic SL(2)
Reference 18
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Observation db44b2da-fc9e-4152-b307-69daa852d3bd · outbound
Isogeny graphs of elliptic curves in characteristic zero A classification of isogeny-torsion graphs ofQ-isogeny classes of elliptic curves.Trans
Reference 19
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Observation dcb72ab3-0618-47d5-8680-3c3740574fcf · outbound
Isogeny graphs of elliptic curves in characteristic zero CM Elliptic Curves: Volcanoes, Reality and Applications
Reference 20
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Observation 04f61ce5-5b62-49b9-81db-ac4f7b2b514e · outbound
Isogeny graphs of elliptic curves in characteristic zero CM Elliptic Curves: Volcanoes, Reality and Applications, Part II
Reference 21
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Observation 341629dc-7e0e-46e6-bd96-cfe030990e41 · outbound
Isogeny graphs of elliptic curves in characteristic zero Cox.Primes of the formx 2 +ny 2
Reference 22
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Observation df9603f1-4ed3-4916-9d3e-14a840294560 · outbound
Isogeny graphs of elliptic curves in characteristic zero Universit´ e Louis Pasteur
Reference 23
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Observation 8435b6e4-37ec-4f03-8b03-1fdbae2a8e8a · outbound
Isogeny graphs of elliptic curves in characteristic zero Exploring isogeny graphs.Habilitation ´ a diriger des recherches
Reference 24
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Observation e51291b7-ec54-4963-9a74-475474d38090 · outbound
Isogeny graphs of elliptic curves in characteristic zero Towards quantum-resistant cryptosystems from supersingular elliptic curve isogenies.J
Reference 25
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Observation d8bd0d9d-9119-4b5e-ab26-847f1cda5650 · outbound
Isogeny graphs of elliptic curves in characteristic zero Galbraith
Reference 26
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Observation a081e2a9-269e-4caa-9b73-8872549c8492 · outbound
Isogeny graphs of elliptic curves in characteristic zero Deligne and M
Reference 27
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Observation fc493f8a-0cd9-419c-8ae5-d64a73161090 · outbound
Isogeny graphs of elliptic curves in characteristic zero Deligne and M
Reference 28
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Observation 5ab465eb-8306-4764-9124-c66d6ba8d13d · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 29
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Observation 579a4acc-e888-482c-a568-9499c930dc0c · outbound
Isogeny graphs of elliptic curves in characteristic zero Faltings
Reference 30
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Observation d096f7ec-74f5-4b60-877c-8112239ee244 · outbound
Isogeny graphs of elliptic curves in characteristic zero Isogeny volcanoes and the SEA algorithm
Reference 31
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Observation 4e0dfef6-f9d8-4209-997c-a301cac32060 · outbound
Isogeny graphs of elliptic curves in characteristic zero Zweiter Teil
Reference 32
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Observation bfb26918-0cf2-4490-86e0-e8d1849d656e · outbound
Isogeny graphs of elliptic curves in characteristic zero Serre’s uniformity question and proper subgroups ofC + ns(p).arXiv e-prints, page arXiv:2305.17780, May 2023
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Observation 215f78d4-bf04-4784-a39c-11e9c6fc5a64 · outbound
Isogeny graphs of elliptic curves in characteristic zero Galbraith.Mathematics of public key cryptography
Reference 34
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Observation 597b0d51-2add-4d48-89c3-7f76d7c46f88 · outbound
Isogeny graphs of elliptic curves in characteristic zero Galbraith and Frederik Vercauteren
Reference 35
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Observation 7286a5e1-9ba0-46a7-bb39-12e6db75fcac · outbound
Isogeny graphs of elliptic curves in characteristic zero Springer-Verlag, New York, 2001
Reference 36
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Observation 880e49fc-dbce-4dba-9fe1-8b6f8cf496e7 · outbound
Isogeny graphs of elliptic curves in characteristic zero Growth of torsion groups of elliptic curves upon base change
Reference 37
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Observation d68c0621-5fa9-4990-86da-acabcc423eb5 · outbound
Isogeny graphs of elliptic curves in characteristic zero An algorithm for determining torsion growth of elliptic curves
Reference 38
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Observation d0dfc9a1-43d4-4a51-9ead-f77e0df0d18a · outbound
Isogeny graphs of elliptic curves in characteristic zero Elliptic curves with surjective adelic Galois representations.Exp
Reference 39
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Observation 6ddd96e4-3f29-4888-bc65-2f7d14792531 · outbound
Isogeny graphs of elliptic curves in characteristic zero Discrete Mathematics and its Applications (Boca Raton)
Reference 40
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Observation 265b59c2-40db-4a44-b8c9-7016d46ea93a · outbound
Isogeny graphs of elliptic curves in characteristic zero ¨ uber das schwache Kartesische Produkt von Graphen.J
Reference 41
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Observation 28cc86e4-6e20-47e6-9433-93f650daa0e3 · outbound
Isogeny graphs of elliptic curves in characteristic zero Cartesian products of directed graphs with loops.Discrete Math., 341(5):1336–1343, 2018
Reference 42
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Observation 100c0c36-1bc8-4214-8866-9d8f15c8a8bd · outbound
Isogeny graphs of elliptic curves in characteristic zero Rational expression forj-invariant function in terms of generators of modular function fields
Reference 43
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Observation abb5dc1f-2cdd-41dd-9113-957dde954b99 · outbound
Isogeny graphs of elliptic curves in characteristic zero Towards quantum-resistant cryptosystems from supersingular elliptic curve iso- genies
Reference 44
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Observation 97e310f9-8c2d-4d62-abb0-5b68ef600b86 · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 45
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Observation a02654f9-4605-4766-86d3-ff8fd20b9068 · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 46
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Observation 2db107ae-5d81-4395-b957-0a22229f1a31 · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 47
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Observation 1bfad2c0-068b-4a6f-b391-2971050667ea · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 48
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Observation 8681bdaf-59d6-4dcd-97de-8985cde46b9b · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 49
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Observation 695b577d-21fc-48f1-8048-e3be79bdac71 · outbound
Isogeny graphs of elliptic curves in characteristic zero Ueber die Transformation siebenter Ordnung der elliptischen Functionen.Math
Reference 50
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Observation 33ae0348-2660-4638-a08c-cf87af47f324 · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 51
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Observation c1c3bed7-5f65-449e-b3ab-e4819ce6c9f0 · outbound
Isogeny graphs of elliptic curves in characteristic zero Elliptic curve cryptosystems.Math
Reference 52
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Observation bec0df13-fb31-4b8e-a2ed-ede2018b4140 · outbound
Isogeny graphs of elliptic curves in characteristic zero ProQuest LLC, Ann Arbor, MI, 1996
Reference 53
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Observation 2dd0e370-72aa-437c-94bf-74092f987550 · outbound
Isogeny graphs of elliptic curves in characteristic zero Akademische Verlagsgesellschaft M
Reference 54
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Observation dcc4e123-1cc2-4eb1-a953-d5994bb921ae · outbound
Isogeny graphs of elliptic curves in characteristic zero Universal bounds on the torsion of elliptic curves.Proc
Reference 55
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Observation b355ea9d-f51b-4dfa-a5aa-e219b3215049 · outbound
Isogeny graphs of elliptic curves in characteristic zero Degree of isogenies of elliptic curves with complex multiplication.J
Reference 56
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Observation 68277fd8-ea38-44dd-b8e7-9ed1fa4a0376 · outbound
Isogeny graphs of elliptic curves in characteristic zero Determinants of subquotients of Galois representations associated with abelian varieties.J
Reference 57
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Observation e933d0fc-ba3b-4717-9eb9-e6824fc57bf2 · outbound
Isogeny graphs of elliptic curves in characteristic zero Ligozat.Courbes modulaires de genre1
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Observation a4176d96-dde1-4c55-ba1f-a9911fa5cc6c · outbound
Isogeny graphs of elliptic curves in characteristic zero The L-functions and modular forms database.https://www.lmfdb.org, 2026
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Observation fc41d2ff-9230-48ac-87cb-874124643ff0 · outbound
Isogeny graphs of elliptic curves in characteristic zero On the field of definition ofp-torsion points on elliptic curves over the rationals
Reference 60
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Observation daf4c637-b1c7-4843-8866-023cf1cb3335 · outbound
Isogeny graphs of elliptic curves in characteristic zero Galois representations attached to elliptic curves with complex multiplication.Al- gebra Number Theory, 16(4):777–837, 2022
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Observation d76321fc-fd7d-46fa-aab5-9641e18ab82f · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 62
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Observation 0b7eaf21-e967-42ba-9acd-8e82bce378f2 · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 63
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Observation 92d23c12-bef4-4523-aa82-e28ee81f304c · outbound
Isogeny graphs of elliptic curves in characteristic zero Courbes de Weil de conducteur 26.C
Reference 64
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Observation 9b64923e-8cf6-46ef-ab91-f43f093532da · outbound
Isogeny graphs of elliptic curves in characteristic zero Bornes pour la torsion des courbes elliptiques sur les corps de nombres.Invent
Reference 65
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Observation fe0a986a-09d5-4f4c-8c64-fccef40f697d · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 66
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Observation 48cae052-4d1d-4a73-8a83-14e8c3088298 · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 67
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Observation adfaf130-91ce-41a0-bb5a-769d5dead3ca · outbound
Isogeny graphs of elliptic curves in characteristic zero Isogenies of prime degree over number fields.Compositio Math., 97(3):329–348, 1995
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Observation f2a263e6-7f56-465c-8b30-cf4a0220e468 · outbound
Isogeny graphs of elliptic curves in characteristic zero Isogenies of non-CM elliptic curves with rationalj-invariants over number fields.Math
Reference 69
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Observation 6867de57-8236-4fd0-9e2b-80e0cd066a5f · outbound
Isogeny graphs of elliptic curves in characteristic zero Number ofk-rational points with givenj-invariant on modular curves
Reference 70
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Observation 0e1fae41-aeee-45a5-bbaa-ab25aa3137bb · outbound
Isogeny graphs of elliptic curves in characteristic zero Degrees of isogenies over prime degree number fields of non-CM elliptic curves with rational j-invariant.J
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Observation bac57a62-8a48-4f50-9b41-371e8a5453c4 · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 72
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Observation 4a6a21e8-2901-4158-8acc-f009320c83b4 · outbound
Isogeny graphs of elliptic curves in characteristic zero Stephen G
Reference 73
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Observation ee555f44-dbb6-4f08-a202-0cbbdd3f5a54 · outbound
Isogeny graphs of elliptic curves in characteristic zero Sutherland, and David Zureick-Brown.ℓ-adic images of Galois for elliptic curves overQ(and an appendix with John Voight).Forum Math
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Observation 2428e8d8-80b4-43f0-87b4-8f910a2b89fb · outbound
Isogeny graphs of elliptic curves in characteristic zero Elliptic curves overQand 2-adic images of Galois.Res
Reference 75
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Observation 938cb5bf-1c61-4d98-ae5c-bcae062bcf50 · outbound
Isogeny graphs of elliptic curves in characteristic zero Graph multiplication.Math
Reference 76
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Observation 6dc23f2b-6583-46c4-adf8-c745f8b74b1a · outbound
Isogeny graphs of elliptic curves in characteristic zero ProQuest LLC, Ann Arbor, MI, 2020
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Observation b22cc289-3be3-4a78-92dd-abe11925189f · outbound
Isogeny graphs of elliptic curves in characteristic zero Galois properties of points of finite order of elliptic curves.Invent
Reference 78
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Observation 9430d445-d0c2-4e22-9467-807c51fa88d5 · outbound
Isogeny graphs of elliptic curves in characteristic zero Springer-Verlag, Berlin-New York, 1980
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Observation c6664368-f2d6-4d2b-a998-0a718475ffd1 · outbound
Isogeny graphs of elliptic curves in characteristic zero Advanced Book Classics
Reference 80
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Observation e203abde-90d6-4b9d-8af9-494e47142a7c · outbound
Isogeny graphs of elliptic curves in characteristic zero 1 ofKanˆ o Memo- rial Lectures
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Observation 0f30b327-8421-49be-8a19-2318fd151d88 · outbound
Isogeny graphs of elliptic curves in characteristic zero Silverberg
Reference 82
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Observation c636ba8e-6ed0-464a-89af-321e5e2e9f5d · outbound
Isogeny graphs of elliptic curves in characteristic zero Silverman.Advanced topics in the arithmetic of elliptic curves, volume 151 ofGraduate Texts in Mathematics
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Observation d294b3d8-478b-4ae6-995d-7f3dce8d2b9a · outbound
Isogeny graphs of elliptic curves in characteristic zero Silverman.The arithmetic of elliptic curves, volume 106 ofGraduate Texts in Mathematics
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Observation be936d24-8f95-45b6-969a-35c754579559 · outbound
Isogeny graphs of elliptic curves in characteristic zero Sutherland
Reference 85
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Observation e7a3005a-b03a-43dc-9df1-6c5a42f41b14 · outbound
Isogeny graphs of elliptic curves in characteristic zero On the lattice of subgroups of finite groups.Trans
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Observation 3ceb20f3-6bc8-4115-88ea-8cf31117672c · outbound
Isogeny graphs of elliptic curves in characteristic zero https://www.sagemath.org
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Observation e0bc57a2-8c6a-4ec7-a3c1-ef98bd98d715 · outbound
Isogeny graphs of elliptic curves in characteristic zero On the number of edges of cyclic subgroup graphs of finite groups.Arch
Reference 88
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Observation ae6d7cf0-258d-4274-9239-c8ec4c5ebafa · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 89
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Observation d3f91e4b-8b95-4752-9ecc-adf6f60a17d4 · outbound
Isogeny graphs of elliptic curves in characteristic zero Springer, Cham, 2021
Reference 90
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Observation dc285d10-76b1-4093-9a5a-6b979f759040 · outbound
Isogeny graphs of elliptic curves in characteristic zero Isogenies over quadratic fields of elliptic curves with rationalj-invariant, 2022
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Observation c1ea4ccc-9064-472d-9349-9eb62d5a77dc · outbound
Isogeny graphs of elliptic curves in characteristic zero Waterhouse
Reference 92
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Observation d4c7dcb9-5268-4ece-b4a5-6f6932fee7eb · outbound
Isogeny graphs of elliptic curves in characteristic zero Classification of modular curves with low gonality
Reference 93
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Observation 397fb8a8-a82e-4bab-8e9b-769aba25c977 · outbound
Isogeny graphs of elliptic curves in characteristic zero Elliptic curves with maximal Galois action on their torsion points.Bull
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Observation 6ba32ed4-05ec-4fcb-bb51-d2cd82ef1608 · outbound
Isogeny graphs of elliptic curves in characteristic zero Unresolved cited work
Reference 476
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