curve #2593

y² + xy = x³ − 44568078723595x + 114463301041673455025

a-invariants: [1, 0, 0, -44568078723595, 114463301041673455025]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 28005183570
discriminant (Δ): 5677299943139103092134344667860489000000
Faltings height: 6.5736
naive height: 105.8977
primes of bad reduction: 2, 3, 5, 7, 13, 19, 53, 61, 167
regulator: 18.7224816969661586268654087639350518521724
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:11:30 UTC
last updated: 2026-09-26 20:11:30 UTC

Witness: 2 independent points log in to add more points →

(3765272, 181572041)
(3954650, 242846345)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=38; A=(3q-p)(p+q)^3=-563625, B=-(p+3q)(p-q)^3=45967831. 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 20:11:30 UTC · history