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SageMath
E = EllipticCurve("cl1")
E.isogeny_class()
Elliptic curves in class 104742.cl
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 104742.cl1 | 104742cj4 | \([1, -1, 1, -102787709, -401080979595]\) | \(1112891236915770073/327888\) | \(35385070656302928\) | \([2]\) | \(6488064\) | \(2.9798\) | |
| 104742.cl2 | 104742cj3 | \([1, -1, 1, -7567709, -3881338059]\) | \(444142553850073/196663299888\) | \(21223542069360793034928\) | \([2]\) | \(6488064\) | \(2.9798\) | |
| 104742.cl3 | 104742cj2 | \([1, -1, 1, -6425069, -6263970987]\) | \(271808161065433/147476736\) | \(15915418446301583616\) | \([2, 2]\) | \(3244032\) | \(2.6332\) | |
| 104742.cl4 | 104742cj1 | \([1, -1, 1, -330989, -133326507]\) | \(-37159393753/49741824\) | \(-5368046274378399744\) | \([2]\) | \(1622016\) | \(2.2867\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 104742.cl have rank \(1\).
Complex multiplication
The elliptic curves in class 104742.cl do not have complex multiplication.Modular form 104742.2.a.cl
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
