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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 287490.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 287490.cs1 | 287490cs3 | \([1, 1, 1, -511350, 140529405]\) | \(5763259856089/5670\) | \(14547668739030\) | \([2]\) | \(3317760\) | \(1.8190\) | |
| 287490.cs2 | 287490cs2 | \([1, 1, 1, -32200, 2150885]\) | \(1439069689/44100\) | \(113148534636900\) | \([2, 2]\) | \(1658880\) | \(1.4725\) | |
| 287490.cs3 | 287490cs1 | \([1, 1, 1, -4820, -83323]\) | \(4826809/1680\) | \(4310420367120\) | \([2]\) | \(829440\) | \(1.1259\) | \(\Gamma_0(N)\)-optimal |
| 287490.cs4 | 287490cs4 | \([1, 1, 1, 8870, 7309277]\) | \(30080231/9003750\) | \(-23101159155033750\) | \([2]\) | \(3317760\) | \(1.8190\) |
Rank
sage: E.rank()
The elliptic curves in class 287490.cs have rank \(1\).
Complex multiplication
The elliptic curves in class 287490.cs do not have complex multiplication.Modular form 287490.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
