curve #2307

y² + xy = x³ − 1106173726505x + 360710231137904025

a-invariants: [1, 0, 0, -1106173726505, 360710231137904025]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 765899310
discriminant (Δ): 30417988133469447014391389390625000000
Faltings height: 5.9080
naive height: 94.8094
primes of bad reduction: 2, 3, 5, 11, 19, 23, 47, 113
regulator: 5.319281750082326981268365886804805362664
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:53:26 UTC
last updated: 2026-09-26 19:53:26 UTC

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

(-1171340, 222607795)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=22; A=(3q-p)(p+q)^3=-1765625, B=-(p+3q)(p-q)^3=6241671. 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 19:53:26 UTC · history