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curve #1282

y² = x³ − x² − 3663040176x + 85314608312976

a-invariants: [0, -1, 0, -3663040176, 85314608312976]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 65930519760
discriminant (Δ): 1353447445911826237480166400
Faltings height: 4.1934
naive height: 77.6783
primes of bad reduction: 2, 3, 5, 7, 31, 97, 421
regulator: 444.349696992221432306849586664494888349097674658
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:25:09 UTC
last updated: 2026-09-24 17:25:09 UTC

Witness: 5 independent points log in to add more points →

(64656, -10897740)
(-10944, 11139660)
(36208, 389004)
(112149/4, 17254755/8)
(-69264, -2594700)

Commentary

Torsion Z/2+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 17:25:09 UTC · history

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