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SageMath
sage: E = EllipticCurve("cq1")
sage: E.isogeny_class()
Elliptic curves in class 94864cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
|---|---|---|---|---|---|
| 94864.cx2 | 94864cq1 | [0, -1, 0, -23536, -1382016] | [] | 138240 | \(\Gamma_0(N)\)-optimal |
| 94864.cx1 | 94864cq2 | [0, -1, 0, -239136, 176030912] | [] | 1520640 |
Rank
sage: E.rank()
The elliptic curves in class 94864cq have rank \(0\).
Complex multiplication
The elliptic curves in class 94864cq do not have complex multiplication.Modular form 94864.2.a.cq
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.
\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
