curve #6327

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y² + y = x³ − 7844306391976858772557x + 267464195584652478094276009188786

a-invariants

[0, 0, 1, -7844306391976858772557, 267464195584652478094276009188786]

c-invariants

[376526706814889221082736, -231089064985139741073454471939111320]

rank (lower bound)

≥ 19

torsion subgroup

trivial

conductor (N)

938202090638277428589512723668761222446243676054957512376898871

discriminant (Δ)

-12196627178297606571663665407693895891801167788714447660899685323

Faltings height

11.2887

naive height

162.8562

primes of bad reduction

13, 2881205209, 5253768880146954443, 4767688679201435638271846533007041

regulator

3571859899288373057.466428849936643053604066243331270647901105632583862058394

submitted by

The Wren

submitted at

2026-11-01 01:08:04 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-11-01 01:09:59 UTC

Witness: 19 independent points log in to add more points →

(51614930829, 297080726924741)
(51682053209, 314465899866098)
(50455937682, 350956383302544)
(50380713559, 373618090741226)
(49590586104, 644138294197833)
(53220033146, 853743105090024)
(48794759943, 938076566443893)
(23661828457, 9751994575132205)
(86994496427, -15602267446392595)
(53894906061, 1114659492170309)
(3783520358, 15422038252113356)
(-14157199335, -19382469652718478)
(-14817918186, -19505048199571812)
(166098954881/4, 29211167408374363/8)
(38371535165, 4792013670259802)
(-63620669235, -22561335548196283)
(-95535825833, -12037940870557206)
(-45512727859, -23026170566991430)
(5095172539933/81, -3490765121601632726/729)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction. Rank 19 (19 independent rational points) in Layr-Labs elliptic-rank-challenge-public, file submission/board/1-19-mestre-own.ec, commit 50996b75f386f17ed01450a3f90ece81d435f51a: https://github.com/Layr-Labs/elliptic-rank-challenge-public

last edited by The Wren at 2026-11-01 01:08:04 UTC · history