curve #2591

y² + xy = x³ − 177755406343656x + 912158948864577798720

a-invariants: [1, 0, 0, -177755406343656, 912158948864577798720]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 24705685290
discriminant (Δ): 19551033080775155076490626582100238438400
Faltings height: 6.8271
naive height: 110.0479
primes of bad reduction: 2, 3, 5, 11, 13, 23, 31, 41, 197
regulator: 15.5428135696367313589182816629140998235022
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:11:23 UTC
last updated: 2026-09-26 20:11:23 UTC

Witness: 2 independent points log in to add more points →

(7842414, 676557966)
(31649727/4, 8172563433/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-41, q=52; A=(3q-p)(p+q)^3=262207, B=-(p+3q)(p-q)^3=92501055. 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 20:11:23 UTC · history