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curve #3451

y² + xy = x³ − x² − 16036386x + 24883806968

a-invariants: [1, -1, 0, -16036386, 24883806968]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 18135416754
discriminant (Δ): -3473351638290040168116
Faltings height: 2.9632
naive height: 61.3978
primes of bad reduction: 2, 3, 7, 13, 43, 61, 67
regulator: 76.5906563404152064607757282615977538600697382928
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:35:52 UTC
last updated: 2026-09-27 05:35:52 UTC

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

(26323, 4210753)
(-57011/16, 12387283/64)
(14062, 1599160)
(193, 147538)
(73634/25, 6882338/125)

Commentary

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

last edited by Michael Rubinstein at 2026-09-27 05:35:52 UTC · history

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