curve #3942

y² + xy = x³ − 3816977694006846500215x + 90766898840468372052595551947817

a-invariants: [1, 0, 0, -3816977694006846500215, 90766898840468372052595551947817]
c-invariants: [183214929312328632010321, -78422600598439495847411049830929369]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 269191330439443485710
discriminant (Δ): 804032660962895826686425363331595871803686807388014670656000
Faltings height: 10.9098
naive height: 160.6948
primes of bad reduction: 2, 5, 7, 13, 17, 43, 53, 79, 139, 569, 1222003
regulator: 7262631.020003616547058926548279448721377903727091232
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:30:56 UTC
last updated: 2026-10-05 04:30:56 UTC

Witness: 7 independent points log in to add more points →

(39844232134, -1391988186708427)
(47907848422, 4226083048063205)
(248104239921286/2209, -3410215633220781489461/103823)
(2996095283356/9, -5102411822408695739/27)
(596122713949/16, -33492270645308013/64)
(108163665732934/3025, 4698726892425522467/166375)
(172151562965662/4489, 266946047114178170823/300763)

Commentary

Unlisted rational-isogeny neighbor of curve#3716 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 7: 7 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 04:30:56 UTC · history