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A modular elliptic curve is a type of elliptic curve E that allows for the parametrization of X0(N) -> E through a modular curve.
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Basically, design in modular form means designing a whole product (see program or software piece) based on modules (functions, classes, and a like). The advantages would be a flexible structure, easy to maintain, debug, upgrade and also customize with respect to changing customer requirememnts.
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They are sets with a finite number of elements. For example the days of the week, or the 12 months of the year. Modular arithmetic is based on finite sets.