curve #2396

y² + xy = x³ − 73127237596x − 6718589281208560

a-invariants: [1, 0, 0, -73127237596, -6718589281208560]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 8592990
discriminant (Δ): 5527296940055837081531319234662400
Faltings height: 5.2035
naive height: 86.6600
primes of bad reduction: 2, 3, 5, 7, 17, 29, 83
regulator: 6.147690265069557724263156266226542418072
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:59:00 UTC
last updated: 2026-09-26 19:59:00 UTC

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

(-187810, 19865090)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-1, q=28; A=(3q-p)(p+q)^3=1673055, B=-(p+3q)(p-q)^3=2024287. 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 19:59:00 UTC · history