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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 14 04:27 EDT 2021. Contains 343872 sequences. (Running on oeis4.)