A366468 A divisibility sequence related to an abelian variety isogenous to a power of an elliptic curve.

1, 1, 4879, 38077, 30072836561, 107933476500157, 4138965919245703746721, 66133907203676573069013283, 956411893315133996067203651053840799, 1641203540496096533681564936955975943520959, 71281475498349438098488103653467744633790545028521199

Offset

1,3

Comments

Let E be the elliptic curve defined by y^2 = x^3 + 8*x^2 + 36*x + 288 and let P be the point (8, -40) on E. Baranczuk-Naskrecki-Verzobio proved that a(n) is the product of all primes > 5 which divide the denominator of the x-coordinate of n*P. - Robin Visser, Oct 22 2023

Links

Table of n, a(n) for n=1..11.

Stefan Baranczuk, Bartosz Naskrecki, and Matteo Verzobio, Divisibility sequences related to abelian varieties isogenous to a power of an elliptic curve, arXiv:2309.09699 [Math.NT], Sep 18 2023.

Prog

(Sage)
def a(n):
    E = EllipticCurve([0, 8, 0, 36, 288])
    ans = 1
    for pp in factor((n*E(8, -40))[0].denominator()):
        if pp[0] > 5: ans *= pp[0]
    return ans  # Robin Visser, Oct 22 2023

Crossrefs

Sequence in context: A259329 A200972 A053396 * A210385 A075294 A206273

Adjacent sequences: A366465 A366466 A366467 * A366469 A366470 A366471

Keyword

nonn

Author

N. J. A. Sloane, Oct 11 2023

Extensions

More terms from Robin Visser, Oct 22 2023

Status

approved