curve #2417

y² + xy = x³ − 40622709985x − 2725529640582775

a-invariants: [1, 0, 0, -40622709985, -2725529640582775]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2372370
discriminant (Δ): 1081180882154725982145140625000000
Faltings height: 5.0637
naive height: 84.8964
primes of bad reduction: 2, 3, 5, 7, 11, 13, 79
regulator: 5.441478977205405787161283590006914562062
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:00:18 UTC
last updated: 2026-09-26 20:00:18 UTC

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

(-320845/4, 33114595/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-1, q=26; A=(3q-p)(p+q)^3=1234375, B=-(p+3q)(p-q)^3=1515591. 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 20:00:19 UTC · history