curve #2361

y² + xy + y = x³ − 264138313223x + 52055939837894006

a-invariants: [1, 0, 1, -264138313223, 52055939837894006]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 163032870
discriminant (Δ): 8791835625547574724429969726562500
Faltings height: 5.3667
naive height: 90.5128
primes of bad reduction: 2, 3, 5, 7, 11, 13, 61, 89
regulator: 7.327047884495483178115789654747984962426
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:56:48 UTC
last updated: 2026-09-26 19:56:48 UTC

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

(859143/4, 577773677/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-14, q=25; A=(3q-p)(p+q)^3=118459, B=-(p+3q)(p-q)^3=3618459. 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 19:56:48 UTC · history