curve #3934

y² + xy + y = x³ − 42680271713389495463x + 107321961710568891319906432656

a-invariants: [1, 0, 1, -42680271713389495463, 107321961710568891319906432656]
c-invariants: [2048653042242695782201, -92726174921004501663763201488301]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/6ℤ
conductor (N): 169544208072571930
discriminant (Δ): 6290547316925032516619201576664998874497575219359031250
Faltings height: 9.8258
naive height: 147.2144
primes of bad reduction: 2, 5, 13, 17, 31, 73, 1609, 1699, 12401
regulator: 50033366.887278857591816188660459919137037651019750
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:29:24 UTC
last updated: 2026-10-05 04:29:24 UTC

Witness: 6 independent points log in to add more points →

(7330301896431089/506944, 572239539587879685673037/360944128)
(114418398534582011/8213956, -35041767429169035765765901/23541197896)
(11385273921069127370/2015201881, -19512974808242450783617035218/90464427639971)
(10311436452230/841, 29136387008350049743/24389)
(471179619531131470/114254721, -46449917427695774268182402/1221268712769)
(523195311365615702570/138619948489, -2175001037509139043436852009/51610563361579013)

Commentary

Unlisted rational-isogeny neighbor of curve#3715 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 6: 6 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 04:29:24 UTC · history