curve #2590

y² + xy = x³ − 56156158514446x + 161688071888990580740

a-invariants: [1, 0, 0, -56156158514446, 161688071888990580740]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 5064510990
discriminant (Δ): 39920618726952768280799141699294488166400
Faltings height: 6.6772
naive height: 106.5911
primes of bad reduction: 2, 3, 5, 7, 11, 19, 23, 29, 173
regulator: 13.6739416141697194816185461236738327122299
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:11:19 UTC
last updated: 2026-09-26 20:11:19 UTC

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

(4137668, 411015866)
(4166396, 205639394)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=48; A=(3q-p)(p+q)^3=1186607, B=-(p+3q)(p-q)^3=52501295. 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 20:11:19 UTC · history