curve #2264

y² + xy + y = x³ − 6477315290793x + 6315735562635032056

a-invariants: [1, 0, 1, -6477315290793, 6315735562635032056]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1854947010
discriminant (Δ): 160781381044851149433514179571289062500
Faltings height: 6.1753
naive height: 100.1116
primes of bad reduction: 2, 3, 5, 7, 17, 19, 23, 29, 41
regulator: 4.074158277156934350654380734638144953747
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:50:39 UTC
last updated: 2026-09-26 19:50:39 UTC

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

(1582985, 169363632)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-46, q=29; A=(3q-p)(p+q)^3=-653429, B=-(p+3q)(p-q)^3=17296875. 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 19:50:39 UTC · history