curve #3095

y² + xy = x³ − 408187825x − 3104856293143

a-invariants: [1, 0, 0, -408187825, -3104856293143]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/10ℤ
conductor (N): 77610
discriminant (Δ): 188267790084341760000000000
Faltings height: 3.8248
naive height: 71.0953
primes of bad reduction: 2, 3, 5, 13, 199
regulator: 5.122020936482039227180369386616991212396
submitted by: David Renshaw
submitted at: 2026-09-26 20:37:04 UTC
last updated: 2026-09-26 20:37:04 UTC

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

(75314, 19795403)

Commentary

Cremona 77610ba1 = LMFDB 77610.bb4: https://www.lmfdb.org/EllipticCurve/Q/77610/bb/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 77610, minimal discriminant 188267790084341760000000000, torsion ℤ/10ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:37:04 UTC · history