# Equivalence of Genus One Models

## `IsEquivalent(model1, model2): ModelG1, ModelG1 -> BoolElt, TransG1`

## `IsEquivalent(cubic1, cubic2): RngMPolElt, RngMPolElt -> BoolElt, TransG1`

Return `true` if and only if the two given cubics (or genus one models of degree 3) are equivalent as genus one models. In other words, that there exists a linear transformation of the ambient projective space ${\mathbb{P}}_{{\mathbb{Q}}}^2$ which takes one cubic to the other, up to scaling. The algorithm is given in [[Fisher, 2006](../../references.md#cite-fisher)].

When true, the transformation is also returned as a tuple (the syntax is explained in Section [Transformations between Genus One Models](transformations.md#transformations), on transformations, below).