curve #2265

y² + xy = x³ − 120646993740130x + 510061711458253880900

a-invariants: [1, 0, 0, -120646993740130, 510061711458253880900]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2217144930
discriminant (Δ): 71577854407938454287744292356096000000
Faltings height: 6.6157
naive height: 108.8853
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 43, 101
regulator: 3.343800012887848183463345240714195787578
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:50:43 UTC
last updated: 2026-09-26 19:50:43 UTC

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

(6349220, 27613070)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-43, q=48; A=(3q-p)(p+q)^3=23375, B=-(p+3q)(p-q)^3=76110671. 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 19:50:43 UTC · history