curve #2619

y² + xy + y = x³ − 1182338999474x + 486409927151398916

a-invariants: [1, 0, 1, -1182338999474, 486409927151398916]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 259549710
discriminant (Δ): 3571682249444523930229353956385998400
Faltings height: 5.8062
naive height: 95.0092
primes of bad reduction: 2, 3, 5, 7, 17, 23, 29, 109
regulator: 18.0386134745782688233569685206620668602776
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:08 UTC
last updated: 2026-09-26 20:13:08 UTC

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

(476460, 176498572)
(518688, 112396468)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-40, q=23; A=(3q-p)(p+q)^3=-535517, B=-(p+3q)(p-q)^3=7251363. 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 20:13:08 UTC · history