Creation of Genus One Models
GenusOneModel(n, seq) : RngIntElt, [ RngElt ] -> ModelG1
GenusOneModel(C) : Crv -> ModelG1
GenusOneModel(f) : RngMPolElt -> ModelG1
GenusOneModel(n, E) : RngIntElt, CrvEll -> ModelG1, Crv, MapSch, MapSch
GenusOneModel(mat) : Mtrx -> ModelG1
GenusOneModel(mats) : [ AlgMatElt ] -> ModelG1
CompleteTheSquare(model) : ModelG1 -> ModelG1
RandomGenusOneModel(n) : RngIntElt -> ModelG1
GenericModel(n) : RngIntElt -> ModelG1
ChangeRing(model, B) : ModelG1, Rng -> ModelG1
CubicFromPoint(E, P) : CrvEll, PtEll -> RngMPolElt, MapSch, Pt
HesseModel(n, seq) : RngIntElt, [ RngElt ] -> ModelG1
DiagonalModel(n, seq) : RngIntElt, [ RngElt ] -> ModelG1
Example CrvG1_generic-model (H124E1)
Predicates on Genus One Models
IsGenusOneModel(f) : RngMPolElt -> BoolElt, ModelG1
IsEquivalent(model1, model2) : ModelG1, ModelG1 -> BoolElt, Tup
Access Functions
Degree(model) : ModelG1 -> RngIntElt
DefiningEquations(model) : ModelG1 -> [ RngMPolElt ]
Equations(model) : ModelG1 -> [ RngMPolElt ]
Matrix(model) : ModelG1 -> Mtrx
Curve(model) : ModelG1 -> Crv
Matrices(model) : ModelG1 -> [ AlgMatElt ]
BaseRing(model) : ModelG1 -> Rng
PolynomialRing(model) : ModelG1 -> RngMPol
Eltseq(model) : ModelG1 -> [ RngElt ]
Minimisation and Reduction
Minimise(model : parameters) : ModelG1 -> ModelG1, Tup
Minimise(f) : RngMPolElt -> RngMPolElt, Tup
pMinimise(f, p) : RngMPolElt, RngIntElt -> RngMPolElt, AlgMatElt
Reduce(model) : ModelG1 -> ModelG1, Tup
ReduceQuadrics(seq) : [RngMPolElt] -> [RngMPolElt], AlgMatElt, AlgMatElt
Genus One Models as Coverings
Jacobian(model) : ModelG1 -> CrvEll
nCovering(model : parameters) : ModelG1 -> Crv, CrvEll, MapSch
AddCubics(cubic1, cubic2 : parameters) : RngMPolElt, RngMPolElt -> RngMPolElt
DoubleGenusOneModel(model) : ModelG1 -> ModelG1
FourToTwoCovering(model : parameters) : ModelG1 -> Crv, Crv, MapSch
Families of Elliptic Curves with Prescribed n-Torsion
RubinSilverbergPolynomials(n, J : parameters) : RngIntElt, RngElt -> RngElt, RngElt
Transformations between Genus One Models
IsTransformation(n, g) : RngIntElt, Tup -> BoolElt, RngElt
RandomTransformation(n : parameters) : RngIntElt -> Tup
g * model : Tup, ModelG1 -> ModelG1
g1 * g2 : Tup, Tup -> Tup
ScalingFactor(g) : Tup -> RngElt
Invariants for Genus One Models
aInvariants(model) : ModelG1 -> [ RngElt ]
bInvariants(model) : ModelG1 -> [ RngElt ]
cInvariants(model) : ModelG1 -> [ RngElt ]
Invariants(model) : ModelG1 -> RngElt, RngElt, RngElt
Discriminant(model) : ModelG1 -> RngElt
SL4Invariants(model) : ModelG1 -> [ RngElt ]
Covariants and Contravariants for Genus One Models
Hessian(model) : ModelG1 -> ModelG1
CoveringCovariants(model) : ModelG1 -> [ RngMPolElt ]
Contravariants(model) : ModelG1 -> ModelG1, ModelG1
HesseCovariants(model, r) : ModelG1 -> ModelG1, ModelG1
HessePolynomials(n, r, invariants : parameters) : RngIntElt, RngIntElt, [RngElt] -> RngElt, RngElt, RngElt
Examples
Example CrvG1_visible-three-sha (H124E2)
Bibliography
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Version: V2.19 of
Wed Apr 24 15:09:57 EST 2013