curve #2646

y² + xy + y = x³ − 117589121448x + 15519339493846006

a-invariants: [1, 0, 1, -117589121448, 15519339493846006]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 28850010
discriminant (Δ): 12134894433777448433101764000000
Faltings height: 5.0195
naive height: 88.0850
primes of bad reduction: 2, 3, 5, 7, 37, 47, 79
regulator: 25.0612859400008175349899679662721362173891
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:15:13 UTC
last updated: 2026-09-26 20:15:13 UTC

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

(-202930, 176240427)
(386270, 166334502)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-16, q=21; A=(3q-p)(p+q)^3=9875, B=-(p+3q)(p-q)^3=2380691. 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 20:15:13 UTC · history