Question 4.4 of Frey and Muller, Arithmetic of Modular Curves and Applications, 1998, asks whether or not the equality "r

- Table of r and deg(phi) for all elliptic curves of conductor < 540.
- In July 2001, I gave a talk at Oberwolfach about the congruence modulus and modular degree.
- Ken Ribet recently proved that if p exactly divides the
conductor of E, then ord
_{p}(r) = ord_{p}(N). - Additional analysis of the above table.

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