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Author: William A. Stein
Does r<sub>E</sub> = deg(phi<sub>E</sub>)?

Does rE = deg(phiE)?

William A. Stein

(This is joint with Amod Agashe and Ken Ribet.)

Question 4.4 of Frey and Muller, Arithmetic of Modular Curves and Applications, 1998, asks whether or not the equality "rE = deg(phiE)" holds. The answer is no; the first counterexample occurs for an elliptic curve of conductor 54. Here is some additional information related to their question:

The Modular Forms Database