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)#
> 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