curve #2458

y² + xy = x³ − 5104099900x − 109346875990000

a-invariants: [1, 0, 0, -5104099900, -109346875990000]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 14360010
discriminant (Δ): 3344883848295319592345664000000
Faltings height: 4.5697
naive height: 78.6735
primes of bad reduction: 2, 3, 5, 7, 19, 59, 61
regulator: 5.472805815816325012831452596968023086093
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:02:49 UTC
last updated: 2026-09-26 20:02:49 UTC

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

(-56158, 456206)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-1, q=20; A=(3q-p)(p+q)^3=418399, B=-(p+3q)(p-q)^3=546399. 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 20:02:50 UTC · history