curve #2206

y² + xy + y = x³ − 66818856874073x + 208501756452243817256

a-invariants: [1, 0, 1, -66818856874073, 208501756452243817256]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 11605423830
discriminant (Δ): 312799218589034135655076818962938476562500
Faltings height: 6.7828
naive height: 107.1126
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 127, 179
regulator: 3.330881857935383502840080358049311987937
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:47:03 UTC
last updated: 2026-09-26 19:47:03 UTC

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

(5141460, 928975252)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-26, q=51; A=(3q-p)(p+q)^3=2796875, B=-(p+3q)(p-q)^3=57979691. 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 19:47:03 UTC · history