curve #3327

y² + xy = x³ − 3395238x + 2407700260

a-invariants: [1, 0, 0, -3395238, 2407700260]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 90538
discriminant (Δ): 31657879232
Faltings height: 2.0670
naive height: 56.7273
primes of bad reduction: 2, 7, 29, 223
regulator: 20.5622253989528665723472328121099234265994
submitted by: David Renshaw
submitted at: 2026-09-26 20:58:23 UTC
last updated: 2026-09-26 20:58:23 UTC

Witness: 2 independent points log in to add more points →

(-330, 59260)
(1304, 13422)

Commentary

Cremona 90538d2 = LMFDB 90538.c2: https://www.lmfdb.org/EllipticCurve/Q/90538/c/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 90538, minimal discriminant 31657879232, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:58:23 UTC · history