curve #2441

y² + xy = x³ − x² − 2855123405955x + 1856887560682445025

a-invariants: [1, -1, 0, -2855123405955, 1856887560682445025]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 38035530
discriminant (Δ): 1004301246039355641279332628900
Faltings height: 5.5427
naive height: 97.6540
primes of bad reduction: 2, 3, 5, 13, 19, 29, 59
regulator: 7.010101014303975718223173385707479858448
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:01:48 UTC
last updated: 2026-09-26 20:01:48 UTC

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

(975700, -241695)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-30, q=29; A=(3q-p)(p+q)^3=-117, B=-(p+3q)(p-q)^3=11706603. 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 20:01:48 UTC · history