curve #2314

y² + xy = x³ − 832437615506x + 268272483401110020

a-invariants: [1, 0, 0, -832437615506, 268272483401110020]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 180681270
discriminant (Δ): 5826626086734714191474163527870054400
Faltings height: 5.7938
naive height: 93.9565
primes of bad reduction: 2, 3, 5, 7, 11, 17, 43, 107
regulator: 5.551254814441785412130494842702542278895
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:53:52 UTC
last updated: 2026-09-26 19:53:52 UTC

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

(392728, 43661086)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-11, q=32; A=(3q-p)(p+q)^3=990927, B=-(p+3q)(p-q)^3=6758095. 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 19:53:52 UTC · history