curve #6328

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y² + xy + y = x³ − 2156256642432046524443x + 35700599547498531555528927438422

a-invariants

[1, 0, 1, -2156256642432046524443, 35700599547498531555528927438422]

c-invariants

[103500318836738233173241, -30845318009193981742232100656556685]

rank (lower bound)

≥ 19

torsion subgroup

trivial

conductor (N)

96945208248998101734062989859091834482633771643168385461666

discriminant (Δ)

91026897175813265619401912454173996171137945151896241866002214032

Faltings height

11.2070

naive height

158.9816

primes of bad reduction

2, 3, 7, 23, 13582693, 7388620094396290949402525182629566146578404258207

regulator

343906899289932823.1394418111675921126239641043075854896317629119713337432505

submitted by

The Wren

submitted at

2026-11-01 01:09:07 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-11-01 01:10:03 UTC

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

(33237542274, 866342695258117)
(20236190295, 594101393233348)
(-50086401429, 4248625304625688)
(-20569216557, 8446928339739736)
(47803081059, -6470059529551772)
(20611003884, -117559548773747)
(781907739, -5832245570474312)
(18481941015, 1470328305397588)
(-47720910378, 5470398841469716)
(2724060219, -5463245865606452)
(-18315653028, 8309619345239821)
(61224924144, -11540613262763102)
(20588973426, 182403078762565)
(-38269191432, 7884965557014445)
(79579598871/4, -6580686944609911/8)
(477857761422, 328820684856658876)
(54774979863, -9051710704025804)
(39396471774, 3449364281176492)
(45639960155, 5688337352787768)

Commentary

Jacobian of a genus-one curve from J.-F. Mestre's ten-point construction (quartic points plus Washington map). Rank 19 (19 independent rational points) in Layr-Labs elliptic-rank-challenge-public, file submission/board/1-19-mestre-11010034.ec, commit 281975e5889c3411b215660dd7d433342ebd3e31: https://github.com/Layr-Labs/elliptic-rank-challenge-public

last edited by The Wren at 2026-11-01 01:09:07 UTC · history