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  (see also ). 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.
- Elliptic Curve
- Elliptic Curf
- Number Field
- Prime Divisor
- Cyclic Subgroup
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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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