

A005523


a(n) = maximal number of rational points on an elliptic curve over GF(q), where q = A246655(n) is the nth prime power > 1.
(Formerly M3757)


0



5, 7, 9, 10, 13, 14, 16, 18, 21, 25, 26, 28, 33, 36, 38, 40, 43, 44, 50, 54, 57, 61, 64, 68, 75, 77, 81, 84, 88, 91, 97, 100, 102, 108, 117, 122, 124, 128, 130, 135, 144, 148, 150, 150
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

The successive values of q are 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, ... (see A246655).


REFERENCES

J. W. P. Hirschfeld, Linear codes and algebraic curves, pp. 3553 of F. C. Holroyd and R. J. Wilson, editors, Geometrical Combinatorics. Pitman, Boston, 1984. See N_q(1) on page 51.
J.P. Serre, Oeuvres, vol. 3, pp. 658663 and 664669.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Table of n, a(n) for n=1..44.
W. C. Waterhouse, Abelian varieties over finite fields, Ann Sci. E.N.S., (4) 2 (1969), 521560.
Eric Weisstein's World of Mathematics, Rational Point.
Wikipedia, Hasse's theorem on elliptic curves


FORMULA

a(n) <= q + 1 + 2*sqrt(q) where q = A246655(n) [Hasse theorem].  Sean A. Irvine, Jun 26 2020


EXAMPLE

a(1) = 5 because 5 is the maximal number of rational points on an elliptic curve over GF(2),
a(2) = 7 because 7 is the maximal number of rational points on an elliptic curve over GF(3),
a(3) = 9 because 9 is the maximal number of rational points on an elliptic curve over GF(4).


CROSSREFS

Cf. A000961, A246655.
Sequence in context: A184110 A138892 A190202 * A037084 A018935 A039501
Adjacent sequences: A005520 A005521 A005522 * A005524 A005525 A005526


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Reworded definition and changed offset so as to clarify the indexing.  N. J. A. Sloane, Jan 08 2017


STATUS

approved



