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SageMath
E = EllipticCurve("cq1")
E.isogeny_class()
Elliptic curves in class 54208.cq
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 54208.cq1 | 54208cy2 | \([0, -1, 0, -11031489, 9895057889]\) | \(1278763167594532/375974556419\) | \(43651030131946295066624\) | \([2]\) | \(3686400\) | \(3.0500\) | |
| 54208.cq2 | 54208cy1 | \([0, -1, 0, 1852591, 1028234033]\) | \(24226243449392/29774625727\) | \(-864216116880176693248\) | \([2]\) | \(1843200\) | \(2.7035\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 54208.cq have rank \(0\).
Complex multiplication
The elliptic curves in class 54208.cq do not have complex multiplication.Modular form 54208.2.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 LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
