curve #2648

y² + xy = x³ − 58566413490x + 5451219604628100

a-invariants: [1, 0, 0, -58566413490, 5451219604628100]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 103032930
discriminant (Δ): 19345501566654581752289856000000
Faltings height: 4.9293
naive height: 85.9939
primes of bad reduction: 2, 3, 5, 7, 11, 13, 47, 73
regulator: 5.06104121346854426426900534466768505798967
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:15:20 UTC
last updated: 2026-09-26 20:15:20 UTC

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

(-272220, 35088510)
(-235428, 78797406)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-13, q=20; A=(3q-p)(p+q)^3=25039, B=-(p+3q)(p-q)^3=1689039. 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 20:15:20 UTC · history