curve #2363

y² + xy = x³ − 453775350356x + 117612485788651920

a-invariants: [1, 0, 0, -453775350356, 117612485788651920]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 425683230
discriminant (Δ): 4291682308755232215502500692889600
Faltings height: 5.4153
naive height: 92.1362
primes of bad reduction: 2, 3, 5, 7, 17, 43, 47, 59
regulator: 4.743445650267770211793794524738085880593
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:56:55 UTC
last updated: 2026-09-26 19:56:55 UTC

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

(366364, 23052316)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=4; A=(3q-p)(p+q)^3=-4690913, B=-(p+3q)(p-q)^3=-4642785. 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 19:56:55 UTC · history