Subsections

• Related Structures
• Boolean Operators
• Change Ground Ring
• Alternative Models

The ring over which E was defined, that is, the parent of its coefficients.

True if and only if E and F are identical, that is, they are defined over the same ring R and have the same coefficients.

Lift(E, K) : GeomEC, Rng -> GeomEc

Given an elliptic curve E defined over a field F together with a map h:F -> K, return an elliptic E' defined over K by applying h to the coefficients of E. If the map h is not defined the coefficients will be coerced into K using the standard map; an error occurs if this fails.

Given an elliptic curve E defined over a field K, this function return a sequence [a, b] of two elements of K defining a short Weierstrass model for a curve E' isomorphic to E.

Given an elliptic curve defined over the rational field Q, this function returns an isomorphic curve E defined over Q but with integral coefficients.

Given an elliptic curve E defined over Q, return a global minimal model for E; that is, an elliptic curve E' in Weierstrass form isomorphic to E, with integer coefficients, and such that the discriminant of E' has minimal p-adic valuation at every prime p.