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%I #11 Aug 25 2022 09:54:35
%S 36,1728,3888,108,2700,15552,21168,576,972,14400,52272,3888,18252,
%T 84672,97200,27,10404,15552,51984,2700,47628,209088,228528,15552,2700,
%U 97344,144,7056,90828,388800,415152,1728,117612,499392,176400,972,49284,623808,657072,43200,181548
%N Conductor of the elliptic curve y^2 = x^3 + n.
%C The discriminant of the elliptic curve y^2 = x^3 - n is -432*n^2 and the rank is A060950(n).
%C 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.
%C Conjectures: (Start)
%C (i) a(27*n) = A356731(n) for all n.
%C (ii) a(n) is divisible by 36, and a(n) = 36 <=> n is a sixth power, a(n) = 108 <=> n is 4 times a sixth power, a(n) = 144 <=> n is 27 times a sixth power; moreover, it seems that a(n) is divisible by 36*n^2 if n is squarefree. (End)
%H Jianing Song, <a href="/A356730/b356730.txt">Table of n, a(n) for n = 1..10000</a>
%H LMFDB, <a href="https://www.lmfdb.org/EllipticCurve/Q/">Elliptic Curves Over Q</a>
%o (PARI) a(n) = ellglobalred(ellinit([0,0,0,0,n]))[1]
%Y Cf. A356731, A060950.
%K nonn
%O 1,1
%A _Jianing Song_, Aug 24 2022
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