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A356731
Conductor of the elliptic curve y^2 = x^3 - n.
2
144, 1728, 972, 432, 10800, 15552, 5292, 576, 3888, 14400, 13068, 972, 73008, 84672, 24300, 432, 41616, 15552, 12996, 10800, 190512, 209088, 57132, 15552, 10800, 97344, 36, 1764, 363312, 388800, 103788, 1728, 470448, 499392, 44100, 3888, 197136, 623808, 164268, 43200, 726192
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)
PROG
(PARI) a(n) = ellglobalred(ellinit([0, 0, 0, 0, -n]))[1]
CROSSREFS
Sequence in context: A223594 A223445 A186934 * A368508 A066445 A008431
KEYWORD
nonn
AUTHOR
Jianing Song, Aug 24 2022
STATUS
approved