curve #2613

y² + xy = x³ − 65060710835880x + 201988338874674638400

a-invariants: [1, 0, 0, -65060710835880, 201988338874674638400]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 3621047430
discriminant (Δ): 831189112439739863769076493376000000
Faltings height: 6.4047
naive height: 107.0326
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 41, 173
regulator: 15.6964662779841475666898583667830582996346
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:46 UTC
last updated: 2026-09-26 20:12:46 UTC

Witness: 2 independent points log in to add more points →

(4654686, 5731422)
(18688143/4, 433213461/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-41, q=44; A=(3q-p)(p+q)^3=4671, B=-(p+3q)(p-q)^3=55885375. 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 20:12:47 UTC · history