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curve #1257

y² + y = x³ + x² − 91658447381330290x + 10680898026770913843165700

a-invariants: [0, 1, 1, -91658447381330290, 10680898026770913843165700]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 29880155097515481
discriminant (Δ): -206952078396272960081069219225390341087592479323
Faltings height: 8.3193
naive height: 128.7841
primes of bad reduction: 3, 11, 17, 19, 23, 53, 101, 929, 24509
regulator: 528.7846468770226828051948255401464015514567402
submitted by: hdeping
submitted at: 2026-09-24 16:30:12 UTC
last updated: 2026-09-24 16:30:12 UTC

Witness: 4 independent points log in to add more points →

(186996257, 282704474596)
(-324588718, 2496844246396)
(50485569884/289, 25995759105164/4913)
(4370229151/25, 593615682449/125)

Commentary

Found by a Mestre-Nagao sieve over the Tate normal form family y^2+(t+1)xy+ty=x^3+tx^2 with torsion Z/5Z, at t=43263/901.

last edited by hdeping at 2026-09-27 08:30:47 UTC · history

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