OFFSET
1,1
COMMENTS
The discriminant of the elliptic curve y^2 = x^3 - n is -432*n^2 and the rank is A060951(n).
a(n*t^6) = a(n) for all t since the elliptic curve y^2 = x^3 - n*t^6 can be written as (y/t^3)^2 = (x/t^2)^3 - n, and the conductor is an invariant of elliptic curves.
Conjectures: (Start)
(i) a(27*n) = A356730(n) for all n.
(ii) a(n) is divisible by 36, and a(n) = 36 <=> n is 27 times a sixth power, a(n) = 108 <=> n is 108 times a sixth power, a(n) = 144 <=> n is a sixth power; moreover, it seems that a(n) is divisible by 36*n^2 if n is squarefree. (End)
LINKS
Jianing Song, Table of n, a(n) for n = 1..10000
LMFDB, Elliptic Curves Over Q
PROG
(PARI) a(n) = ellglobalred(ellinit([0, 0, 0, 0, -n]))[1]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jianing Song, Aug 24 2022
STATUS
approved