curve #3297

y² + xy + y = x³ + x² − 25070x + 1517402

a-invariants: [1, 1, 1, -25070, 1517402]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 36465
discriminant (Δ): 1203345
Faltings height: 0.9151
naive height: 42.0019
primes of bad reduction: 3, 5, 11, 13, 17
regulator: 11.3151936784176756684699343975395050353136
submitted by: David Renshaw
submitted at: 2026-09-26 20:53:32 UTC
last updated: 2026-09-26 20:53:32 UTC

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

(-9, 1324)
(116, 374)

Commentary

Cremona 36465k1 = LMFDB 36465.e3: https://www.lmfdb.org/EllipticCurve/Q/36465/e/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 36465, minimal discriminant 1203345, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:53:32 UTC · history