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%I #15 Oct 18 2016 11:59:04
%S 22,23,26,28,29,30,31,33,35,37,39,40,41,46,47,48,50,59,71
%N Numbers N such that the modular curve X_0(N) is hyperelliptic.
%C "The only case where the hyperelliptic involution is not defined by an element of SL(2, R) is N=37."
%C "For N = 40, 48 the hyperelliptic involution v is not of Atkin-Lehner type. The remaining sixteen values are listed in the table below, together with their genera and hyperelliptic involutions v." (see Ogg link)
%C n N g v
%C 1 22 2 11
%C 2 23 2 23
%C 3 26 2 26
%C 4 28 2 7
%C 5 29 2 29
%C 6 30 3 15
%C 7 31 2 31
%C 8 33 3 11
%C 9 35 3 35
%C 10 39 3 39
%C 11 41 3 41
%C 12 46 5 23
%C 13 47 4 47
%C 14 50 2 50
%C 15 59 5 59
%C 16 71 6 71
%H Andrew P. Ogg, <a href="http://www.numdam.org/item?id=BSMF_1974__102__449_0">Hyperelliptic modular curves</a>, Bulletin de la S. M. F., 102 (1974), p. 449-462.
%Y Cf. A001617, A260990.
%K nonn,fini,full
%O 1,1
%A _Gheorghe Coserea_, Oct 17 2016