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curve #1258

y² + xy + y = x³ + x² − 905217443730x + 331494800559601951

a-invariants: [1, 1, 1, -905217443730, 331494800559601951]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 303390855746
discriminant (Δ): 59015953037335254059795279660032
Faltings height: 5.4082
naive height: 94.2079
primes of bad reduction: 2, 11, 37, 59, 61, 103561
regulator: 526.7377672144578085159360774166064044318410741
submitted by: hdeping
submitted at: 2026-09-24 16:30:46 UTC
last updated: 2026-09-24 16:30:46 UTC

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

(4950319/9, 14636317/27)
(972433, 608439507)
(548933, -116441)
(87922219/289, 1425372566301/4913)

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=45628/-629.

last edited by hdeping at 2026-09-27 08:29:10 UTC · history

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