Paper Citation Record · LEDGER

Minimal torsion curves in geometric isogeny classes

As of 23 August 2026, this Paper Citation Record lists 41 of 41 outbound references and 0 inbound Pith citation observations for arXiv:2407.14322.

A citation records a reference. It does not transfer a finding from one paper to another.

pith.paper-citation-record.v1
2407.14322 v2

Coverage vector

measured 41 of 41 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-05-23T22:45:05.501712Z

measured 41 of 41 standing notices

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Source: scholarly_work_events, retraction_status_cache, observed 2026-08-23T06:30:58.430688+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

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measured 0 of 1 external citation measurements

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Source: cited_works

Reference resolution

41 of 41 outbound references displayed

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External citation measurements

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Outbound references

Observation d68bd018-0cf3-410f-83bd-de2577488173 · outbound

This paper cites Steﬀen M¨ uller, J an Tuitman, and Jan Vonk, Explicit Chabauty-Kim for the split Cartan modular curve of level 13 , Ann.

Minimal torsion curves in geometric isogeny classes Steﬀen M¨ uller, J an Tuitman, and Jan Vonk, Explicit Chabauty-Kim for the split Cartan modular curve of level 13 , Ann

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.336623Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a2359610-ee95-4cff-9e6f-6f4ad258c995 · outbound

This paper cites an unresolved cited work.

Minimal torsion curves in geometric isogeny classes Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-05-23T22:45:51.284228Z

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Observation 722fd6b8-d981-4279-a726-a4863850ca6e · outbound

This paper cites Clark, Torsion points and Galois representations on CM elliptic cu rves, Paciﬁc J.

Minimal torsion curves in geometric isogeny classes Clark, Torsion points and Galois representations on CM elliptic cu rves, Paciﬁc J

Reference 3

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.243216Z

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Observation 702b310b-83f7-4d7e-a797-1a69baf26a68 · outbound

This paper cites an unresolved cited work.

Minimal torsion curves in geometric isogeny classes Unresolved cited work

Reference 4

Resolution: unresolved; raw_fallback, observed 2026-05-23T22:45:51.273888Z

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Observation 752fc251-286d-4911-91ab-11ddfc5db08e · outbound

This paper cites Clark, and James Stankewicz, Torsion points on CM elliptic curves over real number ﬁelds, Trans.

Minimal torsion curves in geometric isogeny classes Clark, and James Stankewicz, Torsion points on CM elliptic curves over real number ﬁelds, Trans

Reference 5

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.247490Z

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Observation f5a1dd63-890f-4b65-a263-817f80dc3177 · outbound

This paper cites an unresolved cited work.

Minimal torsion curves in geometric isogeny classes Unresolved cited work

Reference 6

Resolution: unresolved; raw_fallback, observed 2026-05-23T22:45:51.263218Z

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Observation 320d9bd5-9ef5-4d61-991d-47845f5fea8d · outbound

This paper cites Odd degree isolated points on $X_1(N)$ with rational $j$-invariant.

Minimal torsion curves in geometric isogeny classes Odd degree isolated points on $X_1(N)$ with rational $j$-invariant

Reference 7

Resolution: verified exact; arxiv_id, observed 2026-05-23T22:45:50.713333Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation da06f579-2e00-4f16-9d6d-a197679a7102 · outbound

This paper cites Sporadic points of odd degree on $X_1(N)$ coming from $\mathbb{Q}$-curves.

Minimal torsion curves in geometric isogeny classes Sporadic points of odd degree on $X_1(N)$ coming from $\mathbb{Q}$-curves

Reference 8

Resolution: verified exact; arxiv_id, observed 2026-05-23T22:45:50.686681Z

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Observation fc706c26-c32f-4dfd-b65d-9c407ff7b36a · outbound

This paper cites an unresolved cited work.

Minimal torsion curves in geometric isogeny classes Unresolved cited work

Reference 9

Resolution: unresolved; raw_fallback, observed 2026-05-23T22:45:51.302157Z

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Observation 24d33afe-c20a-4de0-ac8e-fcb4b147592c · outbound

This paper cites London Math.

Minimal torsion curves in geometric isogeny classes London Math

Reference 10

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.251287Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 67de3114-b05e-4683-8833-8ceaffd2d871 · outbound

This paper cites Clark, CM elliptic curves: volcanoes, reality, and applications , preprint, available at http://alpha.math.uga.edu/~pete/Isogenies.pdf.

Minimal torsion curves in geometric isogeny classes Clark, CM elliptic curves: volcanoes, reality, and applications , preprint, available at http://alpha.math.uga.edu/~pete/Isogenies.pdf

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.235210Z

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Observation 77dd584f-0f02-47b8-a6b6-c75957e5c12e · outbound

This paper cites Clark, Tyler Genao, Paul Pollack, and Frederick S aia, The least degree of a CM point on a modular curve , J.

Minimal torsion curves in geometric isogeny classes Clark, Tyler Genao, Paul Pollack, and Frederick S aia, The least degree of a CM point on a modular curve , J

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.277535Z

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Observation 05c82b24-6f86-4214-af87-fefe45780ec5 · outbound

This paper cites Cox, Primes of the form x2 + ny2, A Wiley-Interscience Publication, John Wiley & Sons Inc., New York, 1989, Fermat, class ﬁeld theory and complex multiplic ation.

Minimal torsion curves in geometric isogeny classes Cox, Primes of the form x2 + ny2, A Wiley-Interscience Publication, John Wiley & Sons Inc., New York, 1989, Fermat, class ﬁeld theory and complex multiplic ation

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.340386Z

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Observation f8614964-bfba-462b-8834-940ef3adac94 · outbound

This paper cites an unresolved cited work.

Minimal torsion curves in geometric isogeny classes Unresolved cited work

Reference 14

Resolution: unresolved; raw_fallback, observed 2026-05-23T22:45:51.231398Z

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Observation de325da0-2934-4c1e-84bb-413aa5122cea · outbound

This paper cites Deligne and M.

Minimal torsion curves in geometric isogeny classes Deligne and M

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.291679Z

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Observation a8ae0e17-88d2-444c-b9f6-45eac34ac2d2 · outbound

This paper cites Proc., vol.

Minimal torsion curves in geometric isogeny classes Proc., vol

Reference 16

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.295495Z

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Observation 68ccf0d0-8956-4f04-8705-ed6580b6d0d8 · outbound

This paper cites 228, Springer-Verlag, New York.

Minimal torsion curves in geometric isogeny classes 228, Springer-Verlag, New York

Reference 17

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.228203Z

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Observation aa6d1583-fb48-404d-b1c6-eeb086f045c2 · outbound

This paper cites an unresolved cited work.

Minimal torsion curves in geometric isogeny classes Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-05-23T22:45:51.266728Z

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Observation 72259763-b9f6-424b-8a06-cab80ed4e977 · outbound

This paper cites 2.2, 2.2.

Minimal torsion curves in geometric isogeny classes 2.2, 2.2

Reference 19

Resolution: verified exact; arxiv_id, observed 2026-05-23T22:45:50.680938Z

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Observation 0792e82b-ea74-4f77-879f-11dda51f8f40 · outbound

This paper cites Polynomial bounds on torsion from a fixed geometric isogeny class of elliptic curves.

Minimal torsion curves in geometric isogeny classes Polynomial bounds on torsion from a fixed geometric isogeny class of elliptic curves

Reference 20

Resolution: verified exact; arxiv_id, observed 2026-05-23T22:45:50.719334Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 92737a55-896c-48d4-82bb-c6a28907ecd0 · outbound

This paper cites Typically bounding torsion on elliptic curves isogenous to rational $j$-invariant.

Minimal torsion curves in geometric isogeny classes Typically bounding torsion on elliptic curves isogenous to rational $j$-invariant

Reference 21

Resolution: verified exact; arxiv_id, observed 2026-05-23T22:45:50.705814Z

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Observation b4afec8d-8673-4eaf-ab88-88e193676f42 · outbound

This paper cites an unresolved cited work.

Minimal torsion curves in geometric isogeny classes Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-05-23T22:45:51.238809Z

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Observation cbeb44c9-eff0-40c4-9198-8df8aac6c426 · outbound

This paper cites an unresolved cited work.

Minimal torsion curves in geometric isogeny classes Unresolved cited work

Reference 23

Resolution: unresolved; raw_fallback, observed 2026-05-23T22:45:51.298974Z

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Observation c8926bcf-abca-4ac9-9f30-31f48d1d58ce · outbound

This paper cites Greenberg, K.

Minimal torsion curves in geometric isogeny classes Greenberg, K

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.305731Z

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Observation 51dcef94-f556-435f-9df6-1672432b4144 · outbound

This paper cites an unresolved cited work.

Minimal torsion curves in geometric isogeny classes Unresolved cited work

Reference 25

Resolution: unresolved; raw_fallback, observed 2026-05-23T22:45:51.287994Z

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Observation 95b184c5-fccb-4a90-a5f5-c40b6e75a740 · outbound

This paper cites 1, 150–160.

Minimal torsion curves in geometric isogeny classes 1, 150–160

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.313455Z

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Observation deb0f304-b757-482c-9093-cdf4e23e136f · outbound

This paper cites Sutherland Jeremy Rouse and David Zureick-Bro wn, ℓ-adic images of Galois for elliptic curves over Q, to appear in Forum Math.

Minimal torsion curves in geometric isogeny classes Sutherland Jeremy Rouse and David Zureick-Bro wn, ℓ-adic images of Galois for elliptic curves over Q, to appear in Forum Math

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.220689Z

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Observation a038d6e1-ed76-48c6-a9c6-1997b03a9d48 · outbound

This paper cites Katz, Galois properties of torsion points on abelian varieties , Invent.

Minimal torsion curves in geometric isogeny classes Katz, Galois properties of torsion points on abelian varieties , Invent

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.224543Z

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Observation 91f4f653-0f2e-4c8b-8d9d-73ac0bd5b518 · outbound

This paper cites 3, 747–771.

Minimal torsion curves in geometric isogeny classes 3, 747–771

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.216133Z

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Observation b23f6af6-a038-45d7-ab01-ccf7c3381cc0 · outbound

This paper cites Galois representations attached to elliptic curves with complex multiplication.

Minimal torsion curves in geometric isogeny classes Galois representations attached to elliptic curves with complex multiplication

Reference 30

Resolution: verified exact; arxiv_id, observed 2026-05-23T22:45:50.693361Z

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Observation 3c2bf858-3897-4d4a-af92-64684c6f92c5 · outbound

This paper cites Mazur, Rational isogenies of prime degree (with an appendix by D.

Minimal torsion curves in geometric isogeny classes Mazur, Rational isogenies of prime degree (with an appendix by D

Reference 31

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.259719Z

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Observation 55f06b70-f150-4474-9dde-b0b4f51c2510 · outbound

This paper cites an unresolved cited work.

Minimal torsion curves in geometric isogeny classes Unresolved cited work

Reference 32

Resolution: unresolved; raw_fallback, observed 2026-05-23T22:45:51.309562Z

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Observation 7e096569-2941-4c11-bb74-f08e0ead0353 · outbound

This paper cites Number Theory 1 (2015), Art.

Minimal torsion curves in geometric isogeny classes Number Theory 1 (2015), Art

Reference 33

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.270097Z

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Observation fdb5ac32-7525-4807-9925-7fed05e39395 · outbound

This paper cites an unresolved cited work.

Minimal torsion curves in geometric isogeny classes Unresolved cited work

Reference 34

Resolution: unresolved; raw_fallback, observed 2026-05-23T22:45:51.329081Z

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Observation d7f6fab0-3425-4e4d-b7a6-062e1b9ce174 · outbound

This paper cites Hautes ´Etudes Sci.

Minimal torsion curves in geometric isogeny classes Hautes ´Etudes Sci

Reference 35

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.255288Z

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Observation d212bc94-a976-4a78-b4ca-60bd0e4e50e2 · outbound

This paper cites an unresolved cited work.

Minimal torsion curves in geometric isogeny classes Unresolved cited work

Reference 36

Resolution: unresolved; raw_fallback, observed 2026-05-23T22:45:51.325651Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation a8ed977b-5938-47e6-95e3-26c94b518557 · outbound

This paper cites Silverman, The arithmetic of elliptic curves , second ed., Graduate Texts in Mathematics, vol.

Minimal torsion curves in geometric isogeny classes Silverman, The arithmetic of elliptic curves , second ed., Graduate Texts in Mathematics, vol

Reference 37

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.280531Z

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Observation 16b73f7d-b6d2-4aae-b29f-9c2680a33327 · outbound

This paper cites Sutherland, A local-global principle for rational isogenies of prime de gree, J.

Minimal torsion curves in geometric isogeny classes Sutherland, A local-global principle for rational isogenies of prime de gree, J

Reference 38

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.318243Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 7add0795-2e5e-4e5b-aa7c-20a6303694b7 · outbound

This paper cites Sigma 4 (2016), e4, 79.

Minimal torsion curves in geometric isogeny classes Sigma 4 (2016), e4, 79

Reference 39

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.321802Z

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Observation b46cad3c-6710-4ac5-8368-56699aabf513 · outbound

This paper cites Sutherland and David Zywina, Modular curves of prime-power level with inﬁnitely many rat ional points, Algebra Number Theory 11 (2017), no.

Minimal torsion curves in geometric isogeny classes Sutherland and David Zywina, Modular curves of prime-power level with inﬁnitely many rat ional points, Algebra Number Theory 11 (2017), no

Reference 40

Resolution: verified fuzzy; raw_fallback, observed 2026-05-23T22:45:51.332983Z

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No event found in the named queried sources as of 2026-08-23T06:30:58.430688+00:00.

Observation 1bdb708d-b108-442e-b699-3f0510a5cb99 · outbound

This paper cites On the possible images of the mod ell representations associated to elliptic curves over Q.

Minimal torsion curves in geometric isogeny classes On the possible images of the mod ell representations associated to elliptic curves over Q

Reference 41

Resolution: verified exact; local_arxiv, observed 2026-05-23T22:45:50.699057Z

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Pith citing papers

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