curve #2300

y² + xy + y = x³ − x² − 1545456098192x + 711606735854187059

a-invariants: [1, -1, 1, -1545456098192, 711606735854187059]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 156158910
discriminant (Δ): 17480413783492033825176764136849000000
Faltings height: 5.9102
naive height: 95.8126
primes of bad reduction: 2, 3, 5, 19, 29, 47, 67
regulator: 5.129073460588351744740282637131856658759
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:53:01 UTC
last updated: 2026-09-26 19:53:01 UTC

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

(-1308783, 702395641)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-57, q=10; A=(3q-p)(p+q)^3=-9032601, B=-(p+3q)(p-q)^3=-8120601. 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 19:53:01 UTC · history