curve #2454

y² + xy = x³ − x² − 6458036625x + 142441162180425

a-invariants: [1, -1, 0, -6458036625, 142441162180425]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 9114210
discriminant (Δ): 8472927320441400368483944532100
Faltings height: 4.6412
naive height: 79.3794
primes of bad reduction: 2, 3, 5, 7, 17, 23, 37
regulator: 7.177037325851498835670519302266544873518
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:02:35 UTC
last updated: 2026-09-26 20:02:35 UTC

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

(69040, 5030595)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-30, q=7; A=(3q-p)(p+q)^3=-620517, B=-(p+3q)(p-q)^3=-455877. 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 20:02:35 UTC · history