curve #3043

y² + xy = x³ − 7595x + 103537

a-invariants: [1, 0, 0, -7595, 103537]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/6ℤ
conductor (N): 115430
discriminant (Δ): 23351489000000
Faltings height: 1.2588
naive height: 38.4193
primes of bad reduction: 2, 5, 7, 17, 97
regulator: 3.56658379527823675700473423056815821768687
submitted by: David Renshaw
submitted at: 2026-09-26 20:34:38 UTC
last updated: 2026-09-26 20:34:38 UTC

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

(84, 203)
(12, 113)

Commentary

Cremona 115430r1 = LMFDB 115430.k3: https://www.lmfdb.org/EllipticCurve/Q/115430/k/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 115430, minimal discriminant 23351489000000, torsion ℤ/6ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:34:38 UTC · history