Invariants for Genus One Models

aInvariants(model): ModelG1 -> [ RngElt ]

The invariants \([a_1, a_2, a_3, a_4, a_6]\) of the given genus one model which must have degree 2, 3, or 4. The formulae in the degree 3 case come from [Artin et al., 2005].

bInvariants(model): ModelG1 -> [ RngElt ]

The invariants \([b_2, b_4, b_6, b_8]\) of the given genus one model which must have degree 2, 3, or 4. These are computed from the aInvariants in the standard way (as for elliptic curves).

cInvariants(model): ModelG1 -> [ RngElt ]

The invariants \([c_4, c_6]\) of the given genus one model. For \(n=2\), 3, or 4 these are the classical invariants, as can be found in [An et al., 2001]. For \(n=5\) the algorithm is described in [Fisher, 2008].

Invariants(model): ModelG1 -> RngElt, RngElt, RngElt

The invariants \(c_4, c_6\) and \(\Delta\) (the discriminant) of the given genus one model.

Discriminant(model): ModelG1 -> RngElt

The discriminant \(\Delta\) of the given genus one model.

SL4Invariants(model): ModelG1 -> [ RngElt ]

The \(SL_4\)-invariants of a genus one model of degree \(4\).