curve #2401

y² + xy + y = x³ − x² − 63019772303x + 5403144980131031

a-invariants: [1, -1, 1, -63019772303, 5403144980131031]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 11932830
discriminant (Δ): 3406356229868532261113144338022400
Faltings height: 5.1643
naive height: 86.2137
primes of bad reduction: 2, 3, 5, 7, 13, 31, 47
regulator: 9.947111350267433677982760968189526509419
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:59:18 UTC
last updated: 2026-09-26 19:59:18 UTC

Witness: 1 independent point log in to add more points →

(-283829, 20756742)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-39, q=8; A=(3q-p)(p+q)^3=-1876833, B=-(p+3q)(p-q)^3=-1557345. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at 2026-09-26 19:59:18 UTC · history