curve #1141

y² = x³ − 10108x + 388368

a-invariants: [0, 0, 0, -10108, 388368]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 484160
discriminant (Δ): 937643622400
Faltings height: 1.1237
naive height: 39.2769
primes of bad reduction: 2, 5, 17, 89
regulator: 10.882789524317104468696836573044075458473773
submitted by: David Renshaw
submitted at: 2026-09-23 21:37:24 UTC
last updated: 2026-09-23 21:37:24 UTC

Witness: 3 independent points log in to add more points →

(64, 60)
(46, 144)
(37, 255)

Commentary

Cremona 484160v2, rank exactly 3 according to Cremona's tables. Witness generators from https://github.com/JohnCremona/ecdata/blob/master/allgens/allgens.480000-489999 . Found by screening the local allgens tables for missing torsion size records; torsion and independence independently verified by the site.

last edited by David Renshaw at 2026-09-23 21:37:24 UTC · history