curve #2203

y² + xy = x³ − 71783561141590x + 213687167546511736100

a-invariants: [1, 0, 0, -71783561141590, 213687167546511736100]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 4113414690
discriminant (Δ): 3947017378665240794588408691264000000000000
Faltings height: 6.9109
naive height: 107.3276
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 37, 149
regulator: 3.501738314084175601549026913466499830215
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:46:51 UTC
last updated: 2026-09-26 19:46:51 UTC

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

(6212300, 2734668890)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-19, q=56; A=(3q-p)(p+q)^3=9472111, B=-(p+3q)(p-q)^3=62859375. 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 19:46:51 UTC · history