curve #2376

y² + xy = x³ − 146582392111x + 21474450964065785

a-invariants: [1, 0, 0, -146582392111, 21474450964065785]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 37332570
discriminant (Δ): 2351854700022095951241299316840000
Faltings height: 5.2379
naive height: 88.7462
primes of bad reduction: 2, 3, 5, 11, 29, 47, 83
regulator: 7.527902610863335497474283380032421104010
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:43 UTC
last updated: 2026-09-26 19:57:43 UTC

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

(338498, 102991001)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=18; A=(3q-p)(p+q)^3=-110473, B=-(p+3q)(p-q)^3=2595575. 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 19:57:43 UTC · history