curve #3933

y² + xy + y = x³ − x² − 4366452718275749371688x + 111032265547841950571296154770667

a-invariants: [1, -1, 1, -4366452718275749371688, 111032265547841950571296154770667]
c-invariants: [209589730477235969841009, -95931877432392291506452315857571977]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/6ℤ
conductor (N): 65902957246370790
discriminant (Δ): 2258222024882152732195838831795961702785046543130343713957478400
Faltings height: 11.1446
naive height: 161.0983
primes of bad reduction: 2, 3, 5, 7, 13, 19, 37, 53, 101, 113, 127, 149
regulator: 4143133.8288675508971301000693543854320466430441017
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:28:54 UTC
last updated: 2026-10-05 04:28:54 UTC

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

(3457672937437/1681, -696271208470255242703/68921)
(-5601739562768706323/123676641, 20208918358804826528326526857/1375407924561)
(42567069647444473/1937664, 13676522340034607344680245/2697228288)
(4163555848357/121, -1644272381848514085/1331)
(8773511638909/225, -815074181842187353/3375)
(2837291973927658237/71250481, -329720736874176203568737503/601425310121)

Commentary

Unlisted rational-isogeny neighbor of curve#3711 (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 04:28:54 UTC · history