curve #2237

y² + xy + y = x³ − x² − 41432293860458x + 102626558312379224681

a-invariants: [1, -1, 1, -41432293860458, 102626558312379224681]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2589817230
discriminant (Δ): 2029976792628159061494504666720997646400
Faltings height: 6.5280
naive height: 105.6788
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 89
regulator: 3.875392621704418816037795023423542011066
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:48:58 UTC
last updated: 2026-09-26 19:48:58 UTC

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

(3794967, 214016071)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-51, q=38; A=(3q-p)(p+q)^3=-362505, B=-(p+3q)(p-q)^3=44413047. 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 19:48:58 UTC · history