curve #3953

y² + xy + y = x³ − x² − 63448609946675921393x + 194527620207538079014473370832

a-invariants: [1, -1, 1, -63448609946675921393, 194527620207538079014473370832]
c-invariants: [3045533277440444226849, -168071863845608000520022993378257]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 18082853740749081030705
discriminant (Δ): 573929210151589088910311287950787405196654591926700625
Faltings height: 9.8463
naive height: 148.4039
primes of bad reduction: 3, 5, 7, 19, 43, 89, 167, 227, 257, 1429, 8101
regulator: 3373374740.68665918549977790661182070499554576465993958
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:33:24 UTC
last updated: 2026-10-05 04:33:24 UTC

Witness: 8 independent points log in to add more points →

(654642100293/121, -130533406396844977/1331)
(7364097795937/1089, -9821980788792588929/35937)
(75511864957/16, 910609733038833/64)
(560214057577/121, -4855264325605975/1331)
(125664244054969/27225, 8910460212489824123/4492125)
(26570723206533/5776, 62699256208457083/438976)
(10171921392897/2209, -71953568091585991/103823)
(44065170048463/8836, 38393764234633485697/830584)

Commentary

Unlisted rational-isogeny neighbor of curve#3671 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 8: 8 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 04:33:24 UTC · history