curve #2398

y² + xy = x³ − 1385099556215x + 627435857769909225

a-invariants: [1, 0, 0, -1385099556215, 627435857769909225]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 93183090
discriminant (Δ): 144111774001956432285102489000000
Faltings height: 5.5055
naive height: 95.4840
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29, 107
regulator: 3.703028989811519055370051604981512641748
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:59:07 UTC
last updated: 2026-09-26 19:59:07 UTC

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

(-708320, 1119797485)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=26; A=(3q-p)(p+q)^3=-2889, B=-(p+3q)(p-q)^3=8152375. 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 19:59:07 UTC · history