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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 11550.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 11550.cs1 | 11550cl3 | \([1, 0, 0, -2300113, 1342486217]\) | \(86129359107301290313/9166294368\) | \(143223349500000\) | \([2]\) | \(245760\) | \(2.1440\) | |
| 11550.cs2 | 11550cl2 | \([1, 0, 0, -144113, 20858217]\) | \(21184262604460873/216872764416\) | \(3388636944000000\) | \([2, 2]\) | \(122880\) | \(1.7975\) | |
| 11550.cs3 | 11550cl4 | \([1, 0, 0, -36113, 51422217]\) | \(-333345918055753/72923718045024\) | \(-1139433094453500000\) | \([2]\) | \(245760\) | \(2.1440\) | |
| 11550.cs4 | 11550cl1 | \([1, 0, 0, -16113, -261783]\) | \(29609739866953/15259926528\) | \(238436352000000\) | \([2]\) | \(61440\) | \(1.4509\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11550.cs have rank \(1\).
Complex multiplication
The elliptic curves in class 11550.cs do not have complex multiplication.Modular form 11550.2.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.
