curve #2611

y² + xy + y = x³ − 2944687744653x + 1943778241181128756

a-invariants: [1, 0, 1, -2944687744653, 1943778241181128756]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 417086670
discriminant (Δ): 1957117331642647582518434847585562500
Faltings height: 5.9006
naive height: 97.7467
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 43
regulator: 8.97260985204571808416584122286684662234423
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:38 UTC
last updated: 2026-09-26 20:12:38 UTC

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

(924077, 107919234)
(1021130, 39593922)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-38, q=27; A=(3q-p)(p+q)^3=-158389, B=-(p+3q)(p-q)^3=11808875. 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 20:12:39 UTC · history