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A169880
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Maximum number of rational points on a smooth absolutely irreducible projective curve of genus 1 over the field F_5^n.
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1
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10, 36, 148, 676, 3237, 15876, 78685, 391876, 1955920, 9771876, 48842100, 244171876, 1220773003, 6103671876, 30517927510, 152588671876, 762941200054, 3814701171876, 19073495062765, 95367451171876, 476837201876328, 2384185888671876, 11920929173444139, 59604645263671876
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = 5^n + 1 + floor(2*5^(n/2)) if 5 does not divide floor(2*5^(n/2)), n is even, or n = 1. Otherwise a(n) = 5^n + floor(2*5^(n/2)) [Deuring-Waterhouse]. - Robin Visser, Aug 17 2023
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PROG
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(Sage)
def a(n):
if (n==1) or (n%2 == 0) or (floor(2*5^(n/2))%5 != 0):
return 5^n + 1 + floor(2*5^(n/2))
else:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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