curve #3973

y² + xy = x³ + x² − 80025570312105652x + 8713470200732161730037760

a-invariants: [1, 1, 0, -80025570312105652, 8713470200732161730037760]
c-invariants: [3841227374981071321, -7528438282241793047110659485]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 368839630407777086661212802
discriminant (Δ): 19402884443970393221032889838904832297311056912
Faltings height: 8.2383
naive height: 128.3770
primes of bad reduction: 2, 3, 7, 11, 19, 23, 29, 97, 139, 227, 263, 463, 10789, 15667
regulator: 1892680037447.055229634074397422971081011137485213539727624
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:37:26 UTC
last updated: 2026-10-05 04:37:26 UTC

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

(224361320016/1369, -628922788352888/50653)
(733846941524/4489, -908748355498348/300763)
(1941331211604/11881, -167860098800084/1295029)
(913245876, 26405867915260)
(9912463562841/4489, 30963705073712911927/300763)
(2457535503369/6889, -2891053498396657817/571787)
(2306013743156/6889, -2520712978673655152/571787)
(2000036523984/3025, -2603329483950411208/166375)
(47343257396/289, 52555551299152/4913)
(4142546358319256391156/25238335345729, 2260360349415442805401668807056/126791768628160398433)

Commentary

Unlisted rational-isogeny neighbor of curve#3621 (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 04:37:26 UTC · history