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curve #1406

y² + xy = x³ − x² − 1539820774172304x + 23256983382057439850628

a-invariants: [1, -1, 0, -1539820774172304, 23256983382057439850628]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/12ℤ
conductor (N): 314242110
discriminant (Δ): 7543885417759431726408052576159531500
Faltings height: 7.0647
naive height: 116.5249
primes of bad reduction: 2, 3, 5, 7, 13, 17, 37, 61
regulator: 81.9942024205345405148930651786066007724623
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:22:24 UTC
last updated: 2026-09-24 23:22:24 UTC

Witness: 2 independent points log in to add more points →

(92637207, 821898062154)
(136644681547309/6007401, 10827205037657611681/14724139851)

Commentary

Torsion Z/12. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 23:22:25 UTC · history

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