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Introduction

This chapter deals with functionality that is specific to elliptic curves defined over the rationals or over number fields. As a general goal, these functions are developed in parallel. Naturally however, the functionality available over Q is far ahead of that available for general number fields, both in the range of functions and in the efficiency of implementations.

Functions declared for number fields may also be used over Q: to do so, it is usually necessary to construct Q as RationalsAsNumberField() rather than Rationals().

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