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A169872
Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 1 over the field F_2^n.
1
5, 9, 14, 25, 44, 81, 150, 289, 558, 1089, 2138, 4225, 8374, 16641, 33130, 66049, 131796, 263169, 525736, 1050625, 2100048, 4198401, 8394400, 16785409, 33566018, 67125249, 134240898, 268468225, 536917252, 1073807361, 2147576330, 4295098369, 8590119956, 17180131329, 34360109096
OFFSET
1,1
LINKS
Max Deuring, Die Typen der Multiplikatorenringe elliptischer Funktionenkörper, Abh. Math. Sem. Hansischen Univ. 14 (1941), 197-272.
Gerard van der Geer et al., Tables of curves with many points
Gerard van der Geer and Marcel van der Vlugt, Tables of curves with many points, Math. Comp. 69 (2000) 797-810.
W. C. Waterhouse, Abelian varieties over finite fields, Ann Sci. E.N.S., (4) 2 (1969), 521-560.
FORMULA
a(n) = 2^n + 1 + floor(2^(n/2 + 1)) if floor(2^(n/2 + 1)) is odd, n is even, or n = 1. Otherwise a(n) = 2^n + floor(2^(n/2 + 1)) [Deuring-Waterhouse]. - Robin Visser, Aug 17 2023
PROG
(Sage)
def a(n):
if (n==1) or (n%2 == 0) or (floor(2^(n/2+1))%2 != 0):
return 2^n + 1 + floor(2^(n/2+1))
else:
return 2^n + floor(2^(n/2+1)) # Robin Visser, Aug 17 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 05 2010
EXTENSIONS
More terms from Robin Visser, Aug 17 2023
STATUS
approved