curve #2256

y² + xy + y = x³ − 9919887249928x − 6180905759427327994

a-invariants: [1, 0, 1, -9919887249928, -6180905759427327994]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 6168032310
discriminant (Δ): 45970175892705561815994668993334320250000
Faltings height: 6.4990
naive height: 101.3903
primes of bad reduction: 2, 3, 5, 11, 17, 47, 149, 157
regulator: 4.790674225363560905385161499664470385670
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:50:09 UTC
last updated: 2026-09-26 19:50:09 UTC

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

(3520465, 1588200887)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-4, q=51; A=(3q-p)(p+q)^3=16300211, B=-(p+3q)(p-q)^3=24789875. 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 19:50:09 UTC · history