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A New Automorphism Of X0(108)

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arxiv 1108.5595 v3 pith:L2LPVIMR submitted 2011-08-29 math.NT

Michael Corin Harrison This is my paper · ORCID
classification math.NT
keywords automorphismautomorphismskenkumomoseactingactionalgebraicanalysis
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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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  1. Point counts, automorphisms, and gonalities of Shimura curves

    math.NT 2025-07 conditional novelty 7.0 of 10

    An algorithm based on Ribet's isogeny computes point counts for Shimura curves, yielding 116 record curves, automorphism results for 9288 of 10609 curves, and a tetragonal classification up to 32 exceptions each.

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