curve #2620

y² + xy = x³ − 805644861595x + 260966012702875025

a-invariants: [1, 0, 0, -805644861595, 260966012702875025]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 913628310
discriminant (Δ): 4045923120658926747505914539289000000
Faltings height: 5.7719
naive height: 93.8583
primes of bad reduction: 2, 3, 5, 7, 23, 43, 53, 83
regulator: 21.1059350162896757335243160098069985511514
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:13:12 UTC
last updated: 2026-09-26 20:13:12 UTC

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

(-891910, 520072205)
(-837970, 590041865)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-53, q=10; A=(3q-p)(p+q)^3=-6599081, B=-(p+3q)(p-q)^3=-5751081. 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 20:13:12 UTC · history