curve #1035

y² + xy = x³ − 101946x + 12401892

a-invariants: [1, 0, 0, -101946, 12401892]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/7ℤ
conductor (N): 762
discriminant (Δ): 1273887851544576
Faltings height: 1.7135
naive height: 46.2102
primes of bad reduction: 2, 3, 127
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:18:39 UTC
last updated: 2026-09-23 15:18:39 UTC

Witness: no points (rank ≥ 0 needs none) log in to add more points →

Commentary

Cremona 762g1 = LMFDB 762.f2: https://www.lmfdb.org/EllipticCurve/Q/762/f/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 762, minimal discriminant 1273887851544576, torsion ℤ/7ℤ.

last edited by David Renshaw at 2026-09-23 15:18:39 UTC · history