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curve #1372

y² = x³ + x² − 13588460785x + 68398329492399

a-invariants: [0, 1, 0, -13588460785, 68398329492399]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 733406508076595441216
discriminant (Δ): 158558440425879979226343800717312
Faltings height: 4.8684
naive height: 81.6111
primes of bad reduction: 2, 17, 89, 223, 257, 2503, 34897
regulator: 1112691.4298981461539240934448641511602887993400283207510
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:40:37 UTC
last updated: 2026-09-24 17:40:37 UTC

Witness: 9 independent points log in to add more points →

(-80059, 25360396)
(-55613, 25536176)
(-34651, 22308028)
(-91789, 23288096)
(-35005, 22386832)
(-7061, 12806032)
(450577, 292270304)
(-142079/16, 878370281/64)
(-5726, 12083797)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:40:37 UTC · history

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