curve #3970

y² = x³ − 13287372306750145998484401x − 9490989457113763330363531016506993760

a-invariants: [0, 0, 0, -13287372306750145998484401, -9490989457113763330363531016506993760]
c-invariants: [637793870724007007927251248, 8200214890946291517434090798262042608640]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 282976117803100217896404857655264
discriminant (Δ): 111226225696164027935178300642208489334940868631883504691098151847176109081664
Faltings height: 13.4802
naive height: 185.1602
primes of bad reduction: 2, 3, 7, 11, 29, 31, 43, 59, 61, 67, 83, 107, 113, 151, 277, 4397, 7417
regulator: 13427262305383.39349494891248558596752525882550930073143874
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:36:42 UTC
last updated: 2026-10-05 04:36:42 UTC

Witness: 10 independent points log in to add more points →

(-4692239022559/4, -16935984631109460105/8)
(-219564008353680345639/82537225, 1988289968905138614342839916484/749850689125)
(-931649989453865431/297025, 186506551947909316992229872/161878625)
(-1973966141272687551/839056, 2273199993480150220327755745/768575296)
(-380131350726639/484, -7224831844430105142895/10648)
(75078508596117630689/10758400, -543983453058207051891100579887/35287552000)
(-1752407740492373532639/2084379025, -99165080053244373793761711475516/95162324386375)
(3926053808785338681/336400, 7365528892463903383386766829/195112000)
(-223612618995498039/80656, -56283649127264464581006715/22906304)
(-2175298025829624452468131135/2582242379061361, -137908708895650331213926753433144802976980/131218632236392557401609)

Commentary

Unlisted rational-isogeny neighbor of curve#3695 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 10: 10 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:36:42 UTC · history