curve #3099

y² + xy = x³ − 920187825x + 6246414106857

a-invariants: [1, 0, 0, -920187825, 6246414106857]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/10ℤ
conductor (N): 77610
discriminant (Δ): 33010505869278473338982400000
Faltings height: 4.1714
naive height: 73.5339
primes of bad reduction: 2, 3, 5, 13, 199
regulator: 2.561010468241019613590184693308495606198
submitted by: David Renshaw
submitted at: 2026-09-26 20:37:13 UTC
last updated: 2026-09-26 20:37:13 UTC

Witness: 1 independent point log in to add more points →

(4554, 1464123)

Commentary

Cremona 77610ba2 = LMFDB 77610.bb3: https://www.lmfdb.org/EllipticCurve/Q/77610/bb/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 77610, minimal discriminant 33010505869278473338982400000, torsion ℤ/10ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:37:14 UTC · history