# Properties

## `AuxiliaryLevel(M): ModSS -> RngIntElt`

The level of the module $M$, where the auxiliary level of `SupersingularModule(N,p)` is, by definition, $N$.

## `BaseRing(M): ModSS -> Rng`

The base ring of the module $M$. (Currently this is always ${\mathbb{Z}}$.)

## `Degree(P): ModSSElt -> RngElt`

The sum of the coefficients of the module element $P$, where $P$ is written with respect the basis of the ambient space of the parent of $M$.

## `Dimension(M): ModSS -> RngIntElt`

The dimension of the module $M$.

## `Eltseq(P): ModSSElt -> SeqEnum`

A sequence of integers that defines the module element $P$.

## `Level(M): ModSS -> RngIntElt`

The level of the module $M$, where the level of `SupersingularModule(N,p)` is, by definition, $Np$.

## `ModularEquation(M): ModSS -> RngMPolElt`

The equation of $X_0(N)$ that we use when using the Mestre method to compute with the module $M$ of supersingular points.

## `Prime(M): ModSS -> RngIntElt`

The prime of the module $M$, where the prime of `SupersingularModule(N,p)` is, by definition, $p$.

## `Example: Properties (ex-b24edc)`

```magma
> M := SupersingularModule(3,11);
> AuxiliaryLevel(M);
11
> BaseRing(M);
Integer Ring
> Degree(M.1+7*M.2);
8
> Dimension(M);
2
> Eltseq(M.1+7*M.2);
[ 1, 7 ]
> Level(M);
33
> Prime(M);
3
> M := SupersingularModule(11,3); M;
Supersingular module associated to X_0(3)/GF(11) of dimension 4
> ModularEquation(M);
x*y + 8

```