curve #2373

y² + xy + y = x³ − 1001923278973x + 386006544861602756

a-invariants: [1, 0, 1, -1001923278973, 386006544861602756]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 14037870
discriminant (Δ): 1497624463101900444408489762562500
Faltings height: 5.5085
naive height: 94.5124
primes of bad reduction: 2, 3, 5, 7, 11, 59, 103
regulator: 7.468153501655425656640825942675506119593
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:57:32 UTC
last updated: 2026-09-26 19:57:32 UTC

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

(-1137665, 231655352)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=27; A=(3q-p)(p+q)^3=12875, B=-(p+3q)(p-q)^3=6941291. 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 19:57:32 UTC · history