normalized eigenform

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Modular elliptic curve — A modular elliptic curve is an elliptic curve E that admits a parametrisation X0(N) → E by a modular curve. This is not the same as a modular curve that happens to be an elliptic curve, and which could be called an elliptic modular… … Wikipedia
Hecke operator — In mathematics, in particular in the theory of modular forms, a Hecke operator, studied by Hecke (1937), is a certain kind of averaging operator that plays a significant role in the structure of vector spaces of modular forms and more… … Wikipedia
Modularity theorem — In mathematics the modularity theorem (formerly called the Taniyama–Shimura–Weil conjecture and several related names) states that elliptic curves over the field of rational numbers are related to modular forms. Andrew Wiles proved the modularity … Wikipedia
Serre conjecture (number theory) — The Quillen–Suslin theorem was also conjectured by Serre, and may also be called Serre s Conjecture. In mathematics, Jean Pierre Serre conjectured the following result regarding two dimensional Galois representations. This was a significant step… … Wikipedia

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