curve #2202

y² + xy = x³ − 223258564855085x + 1283905602228088734225

a-invariants: [1, 0, 0, -223258564855085, 1283905602228088734225]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 678407730
discriminant (Δ): 89226700671455334895457331295122609000000
Faltings height: 6.9088
naive height: 110.7317
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 29, 41
regulator: 5.433132193217655142304038522948053658232
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:46:47 UTC
last updated: 2026-09-26 19:46:47 UTC

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

(8526640, 417099895)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-41, q=54; A=(3q-p)(p+q)^3=445991, B=-(p+3q)(p-q)^3=103742375. 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 19:46:47 UTC · history