curve #3937

y² = x³ + x² − 1147625x + 471662119

a-invariants: [0, 1, 0, -1147625, 471662119]
c-invariants: [55086016, -407846586880]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 323366397056
discriminant (Δ): 473367014391160832
Faltings height: 2.2633
naive height: 53.4732
primes of bad reduction: 2, 17, 73, 89, 257
regulator: 49559.627401422329610116803741163084673567885378670
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:29:55 UTC
last updated: 2026-10-05 04:29:55 UTC

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

(2802, -138791)
(2274, -98113)
(5853/4, -351227/8)
(1122, -24449)
(2661/4, 13991/8)
(2901/4, -36961/8)

Commentary

Unlisted rational-isogeny neighbor of curve#3757 (source contributor: jesper-petersen). 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 04:29:55 UTC · history