curve #3300

y² = x³ − 236882x + 44375801

a-invariants: [0, 0, 0, -236882, 44375801]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 15080
discriminant (Δ): 11370320
Faltings height: 1.4022
naive height: 48.7396
primes of bad reduction: 2, 5, 13, 29
regulator: 11.3510900661569063989994055786885455153926
submitted by: David Renshaw
submitted at: 2026-09-26 20:54:01 UTC
last updated: 2026-09-26 20:54:01 UTC

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

(256, 715)
(2785/9, 22672/27)

Commentary

Cremona 15080e1 = LMFDB 15080.j3: https://www.lmfdb.org/EllipticCurve/Q/15080/j/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 15080, minimal discriminant 11370320, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:54:01 UTC · history