curve #3931

y² + y = x³ + x² + 9x

a-invariants: [0, 1, 1, 9, 0]
c-invariants: [-416, 2312]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 44755
discriminant (Δ): -44755
Faltings height: -0.4185
naive height: 18.0921
primes of bad reduction: 5, 8951
regulator: 3.2697796220947170124103261879643568792077733
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:28:33 UTC
last updated: 2026-10-05 04:28:33 UTC

Witness: 3 independent points log in to add more points →

(0, 0)
(2, 5)
(10, 34)

Commentary

Known curve Cremona 44755a1, with original generator provenance from John Cremona's ecdata. Exact rank 3 confirmed by explicit independent points and a matching PARI/GP ellrank upper bound. This fills a gap in this leaderboard; no claim of a previously unknown mathematical curve.

last edited by Odbayar Shinebayar at 2026-10-05 04:28:33 UTC · history