curve #3974

y² + xy + y = x³ − 51416193426868648x + 4474837194445691856407078

a-invariants: [1, 0, 1, -51416193426868648, 4474837194445691856407078]
c-invariants: [2467977284489695081, -3866259339703043690670258229]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 10817942205250900617851910
discriminant (Δ): 48767865638933426457990098696762940018716306250000
Faltings height: 8.4001
naive height: 127.0498
primes of bad reduction: 2, 3, 5, 11, 19, 61, 83, 131, 191, 229, 349, 359, 479, 991
regulator: 28184030706319.19929560669323269200220122964074474912346892
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:37:36 UTC
last updated: 2026-10-05 04:37:36 UTC

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

(3728644669/25, -44025816791513/125)
(7204437715069/52441, -769667763938893045/12008989)
(231425960463344026/1690607689, 2805927329310308829728035/69512716348613)
(287127052354/1681, 56656290818169070/68921)
(1847716232367154/6528025, 59196693618453124437082/16679103875)
(680325699811785673/3646831321, 258256886445222464960433547/220228496643869)
(1681398488830777/11744329, -8838844801334167482691/40247815483)
(32584108361939766867949/133430660385961, 3923851537008056754668573990824205/1541286779432860036459)
(282811541717393837784781/537961496836009, 138229795535554936534291548236281235/12477477343729902237973)
(51167670777092848463879401/32643887991289, 366010288580141107375505518131970803365/186510299092133849587)

Commentary

Unlisted rational-isogeny neighbor of curve#3618 (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 04:37:36 UTC · history