curve #2200

y² + xy + y = x³ − 87060366164934x + 289195107506978477896

a-invariants: [1, 0, 1, -87060366164934, 289195107506978477896]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 46835765130
discriminant (Δ): 6102172071390464281522707771579286416627600
Faltings height: 6.9517
naive height: 107.9065
primes of bad reduction: 2, 3, 5, 7, 11, 19, 37, 151, 191
regulator: 3.385938480687023085811824225896720950957
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:46:40 UTC
last updated: 2026-09-26 19:46:40 UTC

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

(6614489, 1648620813)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-20, q=57; A=(3q-p)(p+q)^3=9674723, B=-(p+3q)(p-q)^3=68936483. 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 19:46:40 UTC · history