curve #2258

y² + xy + y = x³ − 9389835078559x + 11036115297549418046

a-invariants: [1, 0, 1, -9389835078559, 11036115297549418046]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 11749095930
discriminant (Δ): 369302589795489317866328734624413564900
Faltings height: 6.2567
naive height: 101.2255
primes of bad reduction: 2, 3, 5, 11, 13, 17, 19, 61, 139
regulator: 9.878077959345381640338400976128573891121
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:50:17 UTC
last updated: 2026-09-26 19:50:17 UTC

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

(1657168, 161978378)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=39; A=(3q-p)(p+q)^3=682907, B=-(p+3q)(p-q)^3=21563195. 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 19:50:17 UTC · history