Abstract
In Part 1 we explain how to construct families of elliptic curves with the same mod 3, 4, or 5 representation as that of a given elliptic curve over Q. In §4 we give equations for the families in the mod 4 case. The mod 3 and mod 5 cases were given in [9] (see also [8]). The results remain true (with the same proofs) with the field of rational numbers replaced by any field whose characteristic does not divide the level.
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Silverberg, A. (1997). Explicit Families of Elliptic Curves with Prescribed Mod N Representations. In: Cornell, G., Silverman, J.H., Stevens, G. (eds) Modular Forms and Fermat’s Last Theorem. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1974-3_15
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DOI: https://doi.org/10.1007/978-1-4612-1974-3_15
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