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curve #1261

y² + y = x³ − x² − 46156944026940x + 120699024146039670762

a-invariants: [0, -1, 1, -46156944026940, 120699024146039670762]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/5ℤ
conductor (N): 1821255243313
discriminant (Δ): -553310210827368569201513731270076123
Faltings height: 6.3319
naive height: 106.0028
primes of bad reduction: 11, 41, 61, 163, 461, 881
regulator: 208.37407349971440115482260219408625242095034
submitted by: hdeping
submitted at: 2026-09-24 16:32:29 UTC
last updated: 2026-09-24 16:32:29 UTC

Witness: 3 independent points log in to add more points →

(25808325862/6561, 20358167126482/531441)
(64189305/16, 19696998117/64)
(72974565445/11449, 11324043648538354/1225043)

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=6683/61.

last edited by hdeping at 2026-09-27 08:32:37 UTC · history

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