A169877 Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 1 over the field F_3^n.
7, 16, 38, 100, 275, 784, 2280, 6724, 19964, 59536, 177989, 532900, 1596849, 4787344, 14356482, 43059844, 129162891, 387459856, 1162329651, 3486902500, 10460557755, 31381413904, 94143792483, 282430599364, 847290450408, 2541869016976, 7625603007884, 22876802020900, 68630393933574
Offset: 1
Keywords
Links
- Robin Visser, Table of n, a(n) for n = 1..2000
- 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.
Programs
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Sage
def a(n): if (n==1) or (n%2 == 0) or (floor(2*3^(n/2))%3 != 0): return 3^n + 1 + floor(2*3^(n/2)) else: return 3^n + floor(2*3^(n/2)) # Robin Visser, Aug 17 2023
Formula
a(n) = 3^n + 1 + floor(2*3^(n/2)) if 3 does not divide floor(2*3^(n/2)), n is even, or n = 1. Otherwise a(n) = 3^n + floor(2*3^(n/2)) [Deuring-Waterhouse]. - Robin Visser, Aug 17 2023
Extensions
More terms from Robin Visser, Aug 17 2023