Paper Citation Record · LEDGER

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$

As of 22 August 2026, this Paper Citation Record lists 35 of 35 outbound references and 0 inbound Pith citation observations for arXiv:2506.19560.

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

pith.paper-citation-record.v1
2506.19560 v1

Coverage vector

measured 35 of 35 reference resolution

Typed states for the displayed outbound observations.

Source: paper_references, paper_reference_links, observed 2026-08-15T18:45:25.082762Z

measured 35 of 35 standing notices

One-hop event checks from named stored sources.

Source: scholarly_work_events, retraction_status_cache, observed 2026-08-22T06:32:14.747728+00:00

measured 0 of 0 inbound itemization

Pith citing papers itemized under the disclosed page cap.

Source: paper_references, paper_reference_links

measured 0 of 1 external citation measurements

A source-named dated measurement, never combined with another source.

Source: cited_works

Reference resolution

35 of 35 outbound references displayed

verified exact4
verified fuzzy20
unresolved11
parse uncertain0
malformed identifier0
metadata mismatch0

External citation measurements

No source-named external measurement is stored.

Outbound references

Observation 7cdb2dac-ecdc-428c-92fa-7648b338d7c3 · outbound

This paper cites Number Theory76(1999), no.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Number Theory76(1999), no

Reference 1

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.570338Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b0e979b2-86d8-47e9-b600-9808b8b66f8b · outbound

This paper cites an unresolved cited work.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Unresolved cited work

Reference 2

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:45:25.562323Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c66b4120-87b5-4e8e-bdb6-dc2cd5661182 · outbound

This paper cites an unresolved cited work.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Unresolved cited work

Reference 3

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:45:25.553869Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation e8311012-d8b8-4f49-99b4-390b8a14bad8 · outbound

This paper cites Math.357(2019), 106824, 33.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Math.357(2019), 106824, 33

Reference 4

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.545782Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation c522136e-1e06-492b-a7e3-64644e6842b9 · outbound

This paper cites Uniform polynomial bounds on torsion from rational geometric isogeny classes.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Uniform polynomial bounds on torsion from rational geometric isogeny classes

Reference 5

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:45:25.323862Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 005537f7-95a8-4559-8b8a-1e3372ce7d68 · outbound

This paper cites Gill, Jeremy Rouse, and Lori D.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Gill, Jeremy Rouse, and Lori D

Reference 6

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.537517Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 81756de8-bbec-414f-b0c4-e17da7f8d96f · outbound

This paper cites Comp.94(2025), no.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Comp.94(2025), no

Reference 7

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.529263Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 2424d9b9-b5fc-4cd1-9e37-c52177b3de32 · outbound

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

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Sporadic points of odd degree on $X_1(N)$ coming from $\mathbb{Q}$-curves

Reference 8

Resolution: unresolved; no resolver link, observed 2026-08-15T18:45:24.990703Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 609e4e18-d8e5-48cd-b1ee-b3a00ddd373d · outbound

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

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Clark,CM elliptic curves: volcanoes, reality, and applications, preprint, available athttp://alpha.math.uga.edu/ ~pete/Isogenies.pdf

Reference 9

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.520846Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5d67645b-37b3-4392-9606-42781c183448 · outbound

This paper cites an unresolved cited work.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Unresolved cited work

Reference 10

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:45:25.511933Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 5a1d0f7f-dbba-4a80-a672-083fc9c0ba1f · outbound

This paper cites Algebra417(2014), 52–71.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Algebra417(2014), 52–71

Reference 11

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.503414Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 0090f325-312a-4373-bde0-60dc40837904 · outbound

This paper cites 228, Springer- Verlag, New York, 2005.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ 228, Springer- Verlag, New York, 2005

Reference 12

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.494484Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 8c87c887-d5ec-4340-848a-1ca9e4cd97cc · outbound

This paper cites Number Theory8(2022), no.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Number Theory8(2022), no

Reference 13

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.485227Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation bc6c6208-fa9f-4cf1-a6e1-96f510bf1741 · outbound

This paper cites Faltings,Endlichkeitss¨ atze f¨ ur abelsche Variet¨ aten ¨ uber Zahlk¨ orpern, Invent.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Faltings,Endlichkeitss¨ atze f¨ ur abelsche Variet¨ aten ¨ uber Zahlk¨ orpern, Invent

Reference 14

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.476735Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 3b584c33-d9d3-4c86-a2f2-30f972f96d8d · outbound

This paper cites Math.85(1994), no.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Math.85(1994), no

Reference 15

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.468557Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation cf786c2d-34ae-48ba-8893-68ba377c7461 · outbound

This paper cites Effective bounds for adelic Galois representations attached to elliptic curves over the rationals.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Effective bounds for adelic Galois representations attached to elliptic curves over the rationals

Reference 16

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:45:25.301956Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4d222e90-a198-4888-898f-959dfd466547 · outbound

This paper cites an unresolved cited work.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Unresolved cited work

Reference 17

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:45:25.459834Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation b0d6f6cb-12c7-4cd4-9719-adf7209594db · outbound

This paper cites an unresolved cited work.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Unresolved cited work

Reference 18

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:45:25.451268Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d51ba68a-0abc-4bd7-b557-af9228ee4a63 · outbound

This paper cites an unresolved cited work.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Unresolved cited work

Reference 19

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:45:25.442126Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6bad8144-b802-41da-94f6-b87c8ded4c65 · outbound

This paper cites Lozano-Robledo,On the field of definition ofp-torsion points on elliptic curves over the rationals, Math.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Lozano-Robledo,On the field of definition ofp-torsion points on elliptic curves over the rationals, Math

Reference 20

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.433199Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 824ede07-4fa0-43ec-a04e-d38ed819c634 · outbound

This paper cites Number Theory2(2016), Paper No.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Number Theory2(2016), Paper No

Reference 21

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.423833Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 86caaee4-a410-4b1b-bcac-4c9e4eb9f56e · outbound

This paper cites an unresolved cited work.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Unresolved cited work

Reference 22

Resolution: unresolved; raw_fallback, observed 2026-08-15T18:45:25.414615Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 59a7af40-a5d0-453a-bfad-3200f41ae7b9 · outbound

This paper cites J.165(2002), 159–178.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ J.165(2002), 159–178

Reference 23

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.405647Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6d6d7676-1f53-441c-8c33-7518c18aa7ea · outbound

This paper cites Najman,Torsion of rational elliptic curves over cubic fields and sporadic points onX 1(n), Math.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Najman,Torsion of rational elliptic curves over cubic fields and sporadic points onX 1(n), Math

Reference 24

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.396409Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 02b42b1c-c8b8-4008-9973-9cedaae6e68d · outbound

This paper cites Ogg,Hyperelliptic modular curves, Bull.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Ogg,Hyperelliptic modular curves, Bull

Reference 25

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.387087Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 890fd84a-b1e8-4855-a1c2-ec9bafd117bf · outbound

This paper cites Sutherland, and David Zureick-Brown,ℓ-adic images of Galois for elliptic curves overQ(and an appendix with John Voight), Forum Math.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Sutherland, and David Zureick-Brown,ℓ-adic images of Galois for elliptic curves overQ(and an appendix with John Voight), Forum Math

Reference 26

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.377442Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 4f609f38-cb49-4cf8-a7dc-7703f51e45e5 · outbound

This paper cites Number Theory1(2015), Paper No.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Number Theory1(2015), Paper No

Reference 27

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.366826Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d959ca05-58e0-4b88-b71b-727c70746619 · outbound

This paper cites Math.15(1972), no.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Math.15(1972), no

Reference 28

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.357094Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation d418e656-ecc6-45c6-ac15-a86429e23c4b · outbound

This paper cites Number Theory9(2023), no.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Number Theory9(2023), no

Reference 29

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.345075Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation a170358c-2d61-42dd-8a05-7cc58bba6ecb · outbound

This paper cites Sutherland,Computing images of Galois representations attached to elliptic curves, Forum Math.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Sutherland,Computing images of Galois representations attached to elliptic curves, Forum Math

Reference 30

Resolution: verified fuzzy; raw_fallback, observed 2026-08-15T18:45:25.334127Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 6be2fabe-d7de-43ec-9083-e3180d62aed9 · outbound

This paper cites an unresolved cited work.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Unresolved cited work

Reference 31

Resolution: verified exact; raw_fallback, observed 2026-08-15T18:45:25.287577Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation afffa1ca-f04b-4b5b-b611-083a748cbe83 · outbound

This paper cites Low Degree Places on the Modular Curve X1(N).

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Low Degree Places on the Modular Curve X1(N)

Reference 32

Resolution: unresolved; no resolver link, observed 2026-08-15T18:45:25.071852Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 5a7fe24f-85c4-4418-99a3-ebadf28c2e04 · outbound

This paper cites an unresolved cited work.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Unresolved cited work

Reference 33

Resolution: unresolved; no resolver link, observed 2026-08-15T18:45:25.075737Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Observation 316c11b0-7c5e-4b91-afc0-ea4ba99ea7ab · outbound

This paper cites Isogenies over quadratic fields of elliptic curves with rational $j$-invariant.

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ Isogenies over quadratic fields of elliptic curves with rational $j$-invariant

Reference 34

Resolution: verified exact; local_arxiv, observed 2026-08-15T18:45:25.132392Z

Source-reported events for the cited work

No event found in the named queried sources as of 2026-08-22T06:32:14.747728+00:00.

Observation 7d3a58b1-d160-43f8-a5bf-5242cae74e15 · outbound

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

Rational isolated $j$-invariants from $X_1(\ell^n)$ and $X_0(\ell^n)$ On the possible images of the mod ell representations associated to elliptic curves over Q

Reference 35

Resolution: unresolved; no resolver link, observed 2026-08-15T18:45:25.082762Z

Source-reported events for the cited work

Unavailable: canonical work link unavailable.

Pith citing papers

No inbound Pith citation observations are available.