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A198393
Rank of hyperelliptic curve y^2 = x^5 - n.
1
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, 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, 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
OFFSET
1,5
COMMENTS
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.
PROG
(Magma) _<x> := PolynomialRing(Rationals());
for n := 1 to 100 do
C := HyperellipticCurve(x^5-n);
J := Jacobian(C);
RankBound(J)
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, Oct 24 2011
STATUS
approved