curve #2213

y² + xy + y = x³ − 46222739341818x + 120709986132931998556

a-invariants: [1, 0, 1, -46222739341818, 120709986132931998556]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 275481570
discriminant (Δ): 25806118818856290962196687311566406250000
Faltings height: 6.6341
naive height: 106.0071
primes of bad reduction: 2, 3, 5, 7, 13, 19, 47, 113
regulator: 3.249476330396368269639677218179566462381
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:47:29 UTC
last updated: 2026-09-26 19:47:29 UTC

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

(3733025, 423371157)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-28, q=47; A=(3q-p)(p+q)^3=1159171, B=-(p+3q)(p-q)^3=47671875. 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 19:47:30 UTC · history