curve #2394

y² + xy = x³ − 76014696771x + 3887874356142465

a-invariants: [1, 0, 0, -76014696771, 3887874356142465]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 512773170
discriminant (Δ): 21580819526958569572877380455566400
Faltings height: 5.2837
naive height: 86.7762
primes of bad reduction: 2, 3, 5, 7, 13, 31, 73, 83
regulator: 5.732150602107560834292368671194043692318
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:58:50 UTC
last updated: 2026-09-26 19:58:50 UTC

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

(9074, 56553965)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-5, q=26; A=(3q-p)(p+q)^3=768663, B=-(p+3q)(p-q)^3=2174743. 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 19:58:51 UTC · history