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curve #1312

y² + xy = x³ + x² − 760684600x + 5663063435500

a-invariants: [1, 1, 0, -760684600, 5663063435500]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 23928676534950
discriminant (Δ): 14314539017856668464287562500
Faltings height: 4.1084
naive height: 72.9628
primes of bad reduction: 2, 3, 5, 11, 23, 31, 41, 43, 83, 139
regulator: 549.89218068956350603643541959036900715856351401525
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:30:16 UTC
last updated: 2026-09-24 17:30:16 UTC

Witness: 6 independent points log in to add more points →

(1035, 2207845)
(27726, 2412476)
(23655, 940085)
(1996, 2036818)
(29530, 2977210)
(1148305/256, 6258146335/4096)

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 17:30:16 UTC · history

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