curve #2356

y² + xy = x³ − 318314295180x + 68900592605216400

a-invariants: [1, 0, 0, -318314295180, 68900592605216400]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 458948490
discriminant (Δ): 13352399247779733424588329024000000
Faltings height: 5.4076
naive height: 91.0725
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 29, 31
regulator: 1.944050606420929501672319791739611237317
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:56:30 UTC
last updated: 2026-09-26 19:56:30 UTC

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

(297360, 23092020)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=20; A=(3q-p)(p+q)^3=-121121, B=-(p+3q)(p-q)^3=3846879. 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 19:56:30 UTC · history