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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 96558.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 96558.cs1 | 96558cu4 | \([1, 0, 0, -2196334, -1253022550]\) | \(661397832743623417/443352042\) | \(785425186877562\) | \([2]\) | \(1638400\) | \(2.1742\) | |
| 96558.cs2 | 96558cu2 | \([1, 0, 0, -138124, -19331476]\) | \(164503536215257/4178071044\) | \(7401707716779684\) | \([2, 2]\) | \(819200\) | \(1.8277\) | |
| 96558.cs3 | 96558cu1 | \([1, 0, 0, -19544, 613680]\) | \(466025146777/177366672\) | \(314215878814992\) | \([2]\) | \(409600\) | \(1.4811\) | \(\Gamma_0(N)\)-optimal |
| 96558.cs4 | 96558cu3 | \([1, 0, 0, 22806, -61656066]\) | \(740480746823/927484650666\) | \(-1643095635218509626\) | \([2]\) | \(1638400\) | \(2.1742\) |
Rank
sage: E.rank()
The elliptic curves in class 96558.cs have rank \(1\).
Complex multiplication
The elliptic curves in class 96558.cs do not have complex multiplication.Modular form 96558.2.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.
