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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 46550.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 46550.cs1 | 46550ca3 | \([1, 0, 0, -104763, 104976017]\) | \(-69173457625/2550136832\) | \(-4687828877312000000\) | \([]\) | \(979776\) | \(2.2628\) | |
| 46550.cs2 | 46550ca1 | \([1, 0, 0, -19013, -1010983]\) | \(-413493625/152\) | \(-279416375000\) | \([]\) | \(108864\) | \(1.1642\) | \(\Gamma_0(N)\)-optimal |
| 46550.cs3 | 46550ca2 | \([1, 0, 0, 11612, -3834608]\) | \(94196375/3511808\) | \(-6455635928000000\) | \([]\) | \(326592\) | \(1.7135\) |
Rank
sage: E.rank()
The elliptic curves in class 46550.cs have rank \(1\).
Complex multiplication
The elliptic curves in class 46550.cs do not have complex multiplication.Modular form 46550.2.a.cs
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.
\(\left(\begin{array}{rrr} 1 & 9 & 3 \\ 9 & 1 & 3 \\ 3 & 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
