curve #2353

y² + xy + y = x³ − x² − 252113790857x − 17337483415841911

a-invariants: [1, -1, 1, -252113790857, -17337483415841911]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 6230070
discriminant (Δ): 895725460886002160990655873024000000
Faltings height: 5.5911
naive height: 90.3730
primes of bad reduction: 2, 3, 5, 7, 11, 29, 31
regulator: 3.404189951534399079660680178438630397101
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:56:18 UTC
last updated: 2026-09-26 19:56:18 UTC

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

(-393603, 144823426)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-3, q=32; A=(3q-p)(p+q)^3=2414511, B=-(p+3q)(p-q)^3=3987375. 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 19:56:18 UTC · history