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curve #1248

y² + xy + y = x³ − 1116897681699x + 453780107075501066

a-invariants: [1, 0, 1, -1116897681699, 453780107075501066]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 6647665425830
discriminant (Δ): 214367423733812848581068462907388100
Faltings height: 5.6834 ☆ record for ℤ/6ℤ torsion, rank ≥ 5
naive height: 94.8383
primes of bad reduction: 2, 5, 11, 13, 29, 173, 193, 4801
regulator: 1165.52060154406462360225006026247299826319743968
submitted by: hdeping
submitted at: 2026-09-24 15:39:53 UTC
last updated: 2026-09-24 15:39:53 UTC

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

(-1126607, -530611572)
(627613, 3717958)
(654601, 55851162)
(4206464, 8375616998)
(1493897236/2025, -16159405457251/91125)

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=-2887/319.

last edited by hdeping at 2026-09-27 08:25:44 UTC · history

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