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curve #1285

y² = x³ − 240037203x + 1193474985298

a-invariants: [0, 0, 0, -240037203, 1193474985298]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 91255685040
discriminant (Δ): 269814241688677625571840000
Faltings height: 3.7913
naive height: 69.5025
primes of bad reduction: 2, 3, 5, 13, 23, 29, 47, 311
regulator: 229.238162882334167400062187240625982714681644277
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:25:40 UTC
last updated: 2026-09-24 17:25:40 UTC

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

(-9751, 1614600)
(-2623, 1343520)
(-5422, 1528254)
(337481/25, 80342496/125)
(-4369, 1469286)

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 17:25:40 UTC · history

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