curve #2282

y² + xy + y = x³ − 53584194364383x + 150974258291314139806

a-invariants: [1, 0, 1, -53584194364383, 150974258291314139806]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 821230410
discriminant (Δ): 11532121383332454203746625726610562500
Faltings height: 6.4270
naive height: 106.4504
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 29, 41
regulator: 4.843681238688760274893633671189387972007
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:51:50 UTC
last updated: 2026-09-26 19:51:50 UTC

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

(4223585, -296928)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-46, q=41; A=(3q-p)(p+q)^3=-21125, B=-(p+3q)(p-q)^3=50704731. 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 19:51:50 UTC · history