cp's OEIS Frontend

A276182 Numbers N such that the modular curve X_0(N) is hyperelliptic.

%I A276182 #19 Mar 22 2025 13:13:03
%S A276182 22,23,26,28,29,30,31,33,35,37,39,40,41,46,47,48,50,59,71
%N A276182 Numbers N such that the modular curve X_0(N) is hyperelliptic.
%C A276182 "The only case where the hyperelliptic involution is not defined by an element of SL(2, R) is N=37."
%C A276182 "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 A276182 n    N    g    v
%C A276182 1    22   2    11
%C A276182 2    23   2    23
%C A276182 3    26   2    26
%C A276182 4    28   2    7
%C A276182 5    29   2    29
%C A276182 6    30   3    15
%C A276182 7    31   2    31
%C A276182 8    33   3    11
%C A276182 9    35   3    35
%C A276182 10   39   3    39
%C A276182 11   41   3    41
%C A276182 12   46   5    23
%C A276182 13   47   4    47
%C A276182 14   50   2    50
%C A276182 15   59   5    59
%C A276182 16   71   6    71
%D A276182 J. S. Balakrishnan, B. Mazur, and N. Dogra, Ogg's torsion conjecture: fifty years later, Bull. Amer. Math. Soc., 62:2 (2025), 235-268.
%H A276182 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 A276182 Cf. A001617, A260990.
%K A276182 nonn,fini,full
%O A276182 1,1
%A A276182 _Gheorghe Coserea_, Oct 17 2016