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

1,5

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.

Links

Table of n, a(n) for n=1..100.

Prog

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

Crossrefs

Cf. A179406, A179407, A179408.

Sequence in context: A069848 A194702 A118682 * A083054 A336921 A297742

Adjacent sequences: A198390 A198391 A198392 * A198394 A198395 A198396

Keyword

nonn

Author

Artur Jasinski, Oct 24 2011

Status

approved