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 A198393 Rank of hyperelliptic curve y^2 = x^5 - n. 1

%I

%S 1,0,0,0,2,0,2,1,0,1,0,1,2,1,0,1,1,2,1,0,2,1,1,1,1,1,1,2,0,0,1,1,1,1,

%T 0,0,2,2,0,1,1,1,2,1,1,2,2,1,0,2,0,0,1,2,1,0,1,1,2,2,1,0,2,1,3,1,2,1,

%U 0,0,1,0,2,3,1,0,2,1,1,0,1,1,2,1,1,3,1,0,1,2,0,0,1,2,1,0,1,1,1,1

%N Rank of hyperelliptic curve y^2 = x^5 - n.

%C If a(n)=0 number of rational points of hyperelliptic curve is finite and if a(n)<>0 then is infinite. For n when a(n)=0 see A198394.

%o (MAGMA) _<x> := PolynomialRing(Rationals());

%o for n := 1 to 100 do

%o C := HyperellipticCurve(x^5-n);

%o J := Jacobian(C);

%o RankBound(J)

%Y Cf. A179406, A179407, A179408.

%K nonn

%O 1,5

%A _Artur Jasinski_, Oct 24 2011

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Last modified April 21 02:10 EDT 2021. Contains 343143 sequences. (Running on oeis4.)