curve #2598

y² + xy = x³ − 141825032984131x + 650094544396376719745

a-invariants: [1, 0, 0, -141825032984131, 650094544396376719745]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 9143194830
discriminant (Δ): 776967267310278346839009104500882305600
Faltings height: 6.7019
naive height: 109.3704
primes of bad reduction: 2, 3, 5, 7, 11, 17, 23, 53, 191
regulator: 18.6909636372170450131261202625976494117269
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:11:49 UTC
last updated: 2026-09-26 20:11:49 UTC

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

(6831706, 192601969)
(6899648, 98909951)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=46; A=(3q-p)(p+q)^3=-65513, B=-(p+3q)(p-q)^3=82475415. 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 20:11:49 UTC · history