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curve #1316

y² + xy + y = x³ − 2525029950154x + 1544364802198527356

a-invariants: [1, 0, 1, -2525029950154, 1544364802198527356]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 16631813290290
discriminant (Δ): -9679212578439711599260811645246400
Faltings height: 5.7152
naive height: 97.2854
primes of bad reduction: 2, 3, 5, 11, 41, 53, 61, 523, 727
regulator: 864.84827947405853788365603234227388284915130512441
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:30:56 UTC
last updated: 2026-09-24 17:30:56 UTC

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

(496333, 642697433)
(904693, 20799593)
(839368, 127262843)
(-1181387, 1697225633)
(29553541/25, 57401166421/125)
(1826893, 1739411513)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 17:30:56 UTC · history

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