curve #2350

y² + xy + y = x³ − x² − 2795291813687x + 1798815721747097999

a-invariants: [1, -1, 1, -2795291813687, 1798815721747097999]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 93423330
discriminant (Δ): 15041362555585089082281738816000000
Faltings height: 5.7442
naive height: 97.5905
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 61
regulator: 3.600344206217148564448106507884826690339
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:56:07 UTC
last updated: 2026-09-26 19:56:07 UTC

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

(958287, 10991266)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-33, q=28; A=(3q-p)(p+q)^3=-14625, B=-(p+3q)(p-q)^3=11576031. 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 19:56:07 UTC · history