curve #2412

y² + xy = x³ − 15893329993206x + 24387677373432979620

a-invariants: [1, 0, 0, -15893329993206, 24387677373432979620]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 166840770
discriminant (Δ): 47797844867062846609064812646400
Faltings height: 5.9498
naive height: 102.8044
primes of bad reduction: 2, 3, 5, 29, 37, 71, 73
regulator: 6.196398433574468649318482053365806039826
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:00:00 UTC
last updated: 2026-09-26 20:00:00 UTC

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

(2335416, 87672270)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=36; A=(3q-p)(p+q)^3=-145, B=-(p+3q)(p-q)^3=27620207. 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 20:00:00 UTC · history