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

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

Author

Artur Jasinski, Oct 24 2011

Keywords

• nonn

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.

Crossrefs

Cf. A179406, A179407, A179408.

Programs

Magma

_ := PolynomialRing(Rationals());
for n := 1 to 100 do
C := HyperellipticCurve(x^5-n);
J := Jacobian(C);
RankBound(J)