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curve #1278

y² = x³ − x² − 57610996x + 145627228420

a-invariants: [0, -1, 0, -57610996, 145627228420]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 38142501720
discriminant (Δ): 3078463525665789459974400
Faltings height: 3.4240
naive height: 65.2213
primes of bad reduction: 2, 3, 5, 23, 29, 41, 59, 197
regulator: 108.264380086691565895756966152674182900717427022
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:24:28 UTC
last updated: 2026-09-24 17:24:28 UTC

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

(-3792, 556370)
(-8507, 141450)
(11296, 967518)
(159048, 63358330)
(2464, 136482)

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 17:24:28 UTC · history

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