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curve #1281

y² + xy = x³ − 245841163x + 993128344817

a-invariants: [1, 0, 0, -245841163, 993128344817]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 63635893350
discriminant (Δ): 524818689149853619236000000
Faltings height: 3.8308
naive height: 69.5742
primes of bad reduction: 2, 3, 5, 29, 101, 241, 601
regulator: 145.706145260184255775995114009327914714094447656
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:24:59 UTC
last updated: 2026-09-24 17:24:59 UTC

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

(902, 878249)
(422678, 274399985)
(52448/49, 293119457/343)
(4394402, 9209654249)
(-17278, -279211)

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 17:24:59 UTC · history

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