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 of a Supersingular Module (ex-b24edc)

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> 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

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