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curve #1247

y² + xy + y = x³ − 23154955922614x + 42885847908685861112

a-invariants: [1, 0, 1, -23154955922614, 42885847908685861112]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 12059599736130
discriminant (Δ): 113077836389549746663046297209184400
Faltings height: 6.1697
naive height: 103.9333
primes of bad reduction: 2, 3, 5, 23, 41, 61, 107, 241, 271
regulator: 1923.06889336958999142072312687754702841871322492
submitted by: hdeping
submitted at: 2026-09-24 15:39:37 UTC
last updated: 2026-09-24 15:39:37 UTC

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

(11115367/4, -5285663/8)
(2747161, -90758071)
(2797425, 54179821)
(2212382185/729, -14835502912157/19683)
(25782587485/2401, -3780949687806943/117649)

Commentary

Found by a Mestre-Nagao sieve over the Tate normal form family y^2+txy+(t+2)y=x^3 with torsion Z/6Z, at t=-5789/123.

last edited by hdeping at 2026-09-27 08:26:00 UTC · history

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