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curve #1242

y² = x³ − 7253421x + 11098497600

a-invariants: [0, 0, 0, -7253421, 11098497600]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 582587812371744
discriminant (Δ): -28788771332679061922496
Faltings height: 3.0100
naive height: 59.7833
primes of bad reduction: 2, 3, 23, 59, 139, 181, 193, 307
regulator: 11941.12189830543871036173596380151552835280100934946
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:38:21 UTC
last updated: 2026-09-24 14:38:21 UTC

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

(-2343, 123414)
(1561, 59830)
(1947, 66006)
(4411, 254810)
(7161, 571290)
(28257/16, 3943569/64)
(29875/9, 4147570/27)

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 14:38:21 UTC · history

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