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curve #1334

y² = x³ − x² − 133633025x + 1039012765761

a-invariants: [0, -1, 0, -133633025, 1039012765761]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 54381804383424
discriminant (Δ): -313595591540181962029498368
Faltings height: 3.7781
naive height: 68.8616
primes of bad reduction: 2, 3, 7, 31, 97, 113, 193, 617
regulator: 3687.006989084779304095501000002054485033391989661065
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:34:01 UTC
last updated: 2026-09-24 17:34:01 UTC

Witness: 7 independent points log in to add more points →

(3953, 756648)
(7859, 688572)
(12309/4, 6484053/8)
(-12319, 903096)
(-3053, 1191020)
(-2893039/289, 5757839064/4913)
(551681/49, 336334104/343)

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 17:34:01 UTC · history

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