curve #3935

y² + xy + y = x³ − 861782420176536131x + 301710590527812632727140082

a-invariants: [1, 0, 1, -861782420176536131, 301710590527812632727140082]
c-invariants: [41365556168473734265, -260677950278078448928959632461]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/6ℤ
conductor (N): 1469940702224254 ☆ record for ℤ/6ℤ torsion, rank ≥ 6
discriminant (Δ): 1636569153702111649585114649544148237065810930973810268
Faltings height: 9.1888
naive height: 135.5069
primes of bad reduction: 2, 13, 19, 23, 29, 31, 37, 97, 101, 397
regulator: 889853.28846175147415382725509290152801855044724451
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:29:34 UTC
last updated: 2026-10-05 04:29:34 UTC

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

(-261362500462/289, 90781430955918524/4913)
(-5028102334/625, 274503822397013836/15625)
(81959694848/289, -43976921850416818/4913)
(-117461638, -20032822220687)
(687720962, -5857761841487)
(-7422474789784/7225, -6225996475924779491/614125)

Commentary

Unlisted rational-isogeny neighbor of curve#3708 (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 04:29:34 UTC · history