curve #2302

y² + xy = x³ − 19503710567240x + 33153044330204865600

a-invariants: [1, 0, 0, -19503710567240, 33153044330204865600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 945489930
discriminant (Δ): 1187597397795152454962675740224000000
Faltings height: 6.1926
naive height: 103.4185
primes of bad reduction: 2, 3, 5, 7, 11, 41, 67, 149
regulator: 3.730103118936810304309933244599687011238
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:53:08 UTC
last updated: 2026-09-26 19:53:08 UTC

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

(2552140, 195400)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-41, q=36; A=(3q-p)(p+q)^3=-18625, B=-(p+3q)(p-q)^3=30587711. 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 19:53:08 UTC · history