curve #3938

y² = x³ + x² − 840828x − 219917852

a-invariants: [0, 1, 0, -840828, -219917852]
c-invariants: [40359760, 189766865600]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 341505273100
discriminant (Δ): 17205418144683872000
Faltings height: 2.3998
naive height: 52.5400
primes of bad reduction: 2, 5, 29, 61, 89, 109, 199
regulator: 38497.883380855486781516749271888533382157916614024
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:30:05 UTC
last updated: 2026-10-05 04:30:05 UTC

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

(-736, 886)
(-6512/9, 86174/27)
(-376, 6574)
(1112, 14878)
(1472, 41642)
(-1267/4, -30709/8)

Commentary

Unlisted rational-isogeny neighbor of curve#3756 (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 04:30:06 UTC · history