curve #2235

y² + xy + y = x³ − 17173631242853x + 27173947884104189756

a-invariants: [1, 0, 1, -17173631242853, 27173947884104189756]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 20863372530
discriminant (Δ): 5166226625532685143680665860241860562500
Faltings height: 6.4420
naive height: 103.0368
primes of bad reduction: 2, 3, 5, 7, 11, 13, 43, 107, 151
regulator: 3.470060088402872232262046126436141423660
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:48:51 UTC
last updated: 2026-09-26 19:48:51 UTC

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

(2624730, 423086347)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=43; A=(3q-p)(p+q)^3=1398411, B=-(p+3q)(p-q)^3=29384875. 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 19:48:51 UTC · history