curve #2718

y² + xy + y = x³ − 84054772633319x + 296417822519634217526

a-invariants: [1, 0, 1, -84054772633319, 296417822519634217526]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 15695192370
discriminant (Δ): 50262916667561959636666584835674681320100
Faltings height: 6.7420
naive height: 107.8011
primes of bad reduction: 2, 3, 5, 11, 13, 17, 29, 41, 181
regulator: 60.074076197109682290701246444236650133404472
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:19:10 UTC
last updated: 2026-09-26 20:19:10 UTC

Witness: 3 independent points log in to add more points →

(-10555911, 2739567832)
(5446020, 419287837)
(5487963, 640201618)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-58, q=41; A=(3q-p)(p+q)^3=-889253, B=-(p+3q)(p-q)^3=63069435. 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 20:19:10 UTC · history