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SageMath
sage: E = EllipticCurve("dg1")
sage: E.isogeny_class()
Elliptic curves in class 55440dg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 55440.bb2 | 55440dg1 | [0, 0, 0, -1287408, 658430768] | [] | 1920000 | \(\Gamma_0(N)\)-optimal |
| 55440.bb1 | 55440dg2 | [0, 0, 0, -3857808, -55137877072] | [] | 9600000 |
Rank
sage: E.rank()
The elliptic curves in class 55440dg have rank \(0\).
Complex multiplication
The elliptic curves in class 55440dg do not have complex multiplication.Modular form 55440.2.a.dg
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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
