curve #2615

y² + xy = x³ − x² − 1779482059425x + 453437466904722825

a-invariants: [1, -1, 0, -1779482059425, 453437466904722825]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 202584690
discriminant (Δ): 271807721997429104734426789160955996900
Faltings height: 6.0709
naive height: 96.2356
primes of bad reduction: 2, 3, 5, 7, 11, 23, 31, 41
regulator: 26.0794766327497880690853012744726335213892
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:12:54 UTC
last updated: 2026-09-26 20:12:54 UTC

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

(264096, 43492995)
(1060087/4, 168678027/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-54, q=23; A=(3q-p)(p+q)^3=-3664293, B=-(p+3q)(p-q)^3=6847995. 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 20:12:54 UTC · history