curve #2385

y² + xy = x³ − 89158402606x + 7690671649388420

a-invariants: [1, 0, 0, -89158402606, 7690671649388420]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 73188570
discriminant (Δ): 19808041457646395178418041362841600
Faltings height: 5.2907
naive height: 87.2546
primes of bad reduction: 2, 3, 5, 7, 13, 17, 19, 83
regulator: 6.004414909115588139864902330229187876293
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:58:16 UTC
last updated: 2026-09-26 19:58:16 UTC

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

(371588, 160651106)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-35, q=16; A=(3q-p)(p+q)^3=-569297, B=-(p+3q)(p-q)^3=1724463. 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 19:58:16 UTC · history