curve #2480

y² + xy + y = x³ − 36818679283x + 2719253442533306

a-invariants: [1, 0, 1, -36818679283, 2719253442533306]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 45042690
discriminant (Δ): 3610576700392350310992562500
Faltings height: 4.6054
naive height: 84.6014
primes of bad reduction: 2, 3, 5, 7, 11, 17, 31, 37
regulator: 4.200764067997474660470224062035369692473
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:04:13 UTC
last updated: 2026-09-26 20:04:13 UTC

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

(-151235, 69562892)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=1; A=(3q-p)(p+q)^3=-1329669, B=-(p+3q)(p-q)^3=-1329125. 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 20:04:13 UTC · history