curve #2426

y² + xy = x³ − x² − 26653050450x − 1141465011637500

a-invariants: [1, -1, 0, -26653050450, -1141465011637500]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 188370
discriminant (Δ): 648893834752809308394363059610000
Faltings height: 5.0006
naive height: 83.6321
primes of bad reduction: 2, 3, 5, 7, 13, 23
regulator: 7.835876899118352439227791527928036979994
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:00:52 UTC
last updated: 2026-09-26 20:00:52 UTC

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

(1296999/4, 1245963015/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-36, q=13; A=(3q-p)(p+q)^3=-912525, B=-(p+3q)(p-q)^3=352947. 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 20:00:52 UTC · history