curve #3268

y² + xy + y = x³ + x² − 59940x − 2513820

a-invariants: [1, 1, 1, -59940, -2513820]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 91245
discriminant (Δ): 11106625274600625
Faltings height: 1.7733
naive height: 44.6169
primes of bad reduction: 3, 5, 7, 11, 79
regulator: 5.23490486873031666510271652223381682343017
submitted by: David Renshaw
submitted at: 2026-09-26 20:48:51 UTC
last updated: 2026-09-26 20:48:51 UTC

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

(-45, 330)
(-52, 708)

Commentary

Cremona 91245c2 = LMFDB 91245.e5: https://www.lmfdb.org/EllipticCurve/Q/91245/e/5 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 91245, minimal discriminant 11106625274600625, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:48:51 UTC · history