Show commands for:
SageMath
sage: E = EllipticCurve("g1")
sage: E.isogeny_class()
Elliptic curves in class 37905.g
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
37905.g1 | 37905k4 | [1, 1, 1, -40620, 3133920] | [2] | 96768 | |
37905.g2 | 37905k2 | [1, 1, 1, -2715, 40872] | [2, 2] | 48384 | |
37905.g3 | 37905k1 | [1, 1, 1, -910, -10390] | [2] | 24192 | \(\Gamma_0(N)\)-optimal |
37905.g4 | 37905k3 | [1, 1, 1, 6310, 264692] | [2] | 96768 |
Rank
sage: E.rank()
The elliptic curves in class 37905.g have rank \(0\).
Complex multiplication
The elliptic curves in class 37905.g do not have complex multiplication.Modular form 37905.2.a.g
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.