curve #2595

y² + xy + y = x³ − x² − 55431903371828x + 158821788052622707031

a-invariants: [1, -1, 1, -55431903371828, 158821788052622707031]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 3110177070
discriminant (Δ): 3902728594008950827680728750703504782400
Faltings height: 6.5936
naive height: 106.5521
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 79
regulator: 15.2586271403323018874186052140262078635156
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:11:38 UTC
last updated: 2026-09-26 20:11:38 UTC

Witness: 2 independent points log in to add more points →

(16900959/4, 1591547411/8)
(4247103, 72188035)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-33, q=46; A=(3q-p)(p+q)^3=375687, B=-(p+3q)(p-q)^3=51769095. 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 20:11:38 UTC · history