curve #2317

y² + xy = x³ − 1225992983646x + 521884716511487940

a-invariants: [1, 0, 0, -1225992983646, 521884716511487940]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 539572110
discriminant (Δ): 274184388475763859271644234389913600
Faltings height: 5.7055
naive height: 95.1179
primes of bad reduction: 2, 3, 5, 7, 11, 37, 59, 107
regulator: 9.309957261020694247225132855737179912798
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:54:01 UTC
last updated: 2026-09-26 19:54:01 UTC

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

(878940, 350734290)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-35, q=24; A=(3q-p)(p+q)^3=-142417, B=-(p+3q)(p-q)^3=7599023. 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 19:54:02 UTC · history