curve #2295

y² + xy + y = x³ − 1648303896389x + 761835457007521436

a-invariants: [1, 0, 1, -1648303896389, 761835457007521436]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 941410470
discriminant (Δ): 35880343499571675962565646104588922500
Faltings height: 5.9526
naive height: 96.0059
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 29, 47
regulator: 5.548654639349195695245142698286340683473
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:52:40 UTC
last updated: 2026-09-26 19:52:40 UTC

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

(-1393851, 593422432)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-58, q=11; A=(3q-p)(p+q)^3=-9447893, B=-(p+3q)(p-q)^3=-8212725. 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 19:52:41 UTC · history