A New Automorphism Of X0(108)

Details A New Automorphism Of X0(108) A New Automorphism Of X0(108)

2011-08-29

arxiv.org/abs/1108.5595v2

Mathematics

Number Theory

v2; some extra comments in the intro on the automorphisms of X0(N) for N!=108

Scientific paper

Let X0(N) denote the modular curve classifying elliptic curves with a cyclic N-isogeny, A0(N) its group of algebraic autmorphisms and B0(N) the subgroup of automorphisms coming from matrices acting on the upper halfplane. In a well-known paper, Kenku and Momose showed that A0(N) and B0(N) are equal (all automorphisms come from matrix action) when X0(N) has genus at least 2, except for N = 37 and 63. However, there is a mistake in their analysis of the N = 108 case. In the style of Kenku and Momose, we show that B0(108) is of index 2 in A0(108) and construct an explicit new automorphism of order 2 on a canonical model of X0(108).

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