curve #2210

y² + xy + y = x³ − 148237353707593x + 694620422680804920056

a-invariants: [1, 0, 1, -148237353707593, 694620422680804920056]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 17312024730
discriminant (Δ): 35555811917496524637321039744902922562500
Faltings height: 6.8159
naive height: 109.5031
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29, 103, 193
regulator: 8.816607023040498117886716754472914499457
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:47:18 UTC
last updated: 2026-09-26 19:47:18 UTC

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

(29430955/4, 11969530351/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-58, q=45; A=(3q-p)(p+q)^3=-424021, B=-(p+3q)(p-q)^3=84139979. 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 19:47:18 UTC · history