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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 35280.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 35280.cs1 | 35280bo4 | \([0, 0, 0, -765723, -242798038]\) | \(282678688658/18600435\) | \(3267148101350676480\) | \([2]\) | \(589824\) | \(2.3022\) | |
| 35280.cs2 | 35280bo2 | \([0, 0, 0, -148323, 17374322]\) | \(4108974916/893025\) | \(78429481170969600\) | \([2, 2]\) | \(294912\) | \(1.9556\) | |
| 35280.cs3 | 35280bo1 | \([0, 0, 0, -139503, 20053838]\) | \(13674725584/945\) | \(20748539992320\) | \([2]\) | \(147456\) | \(1.6090\) | \(\Gamma_0(N)\)-optimal |
| 35280.cs4 | 35280bo3 | \([0, 0, 0, 327957, 106057658]\) | \(22208984782/40516875\) | \(-7116749217365760000\) | \([2]\) | \(589824\) | \(2.3022\) |
Rank
sage: E.rank()
The elliptic curves in class 35280.cs have rank \(1\).
Complex multiplication
The elliptic curves in class 35280.cs do not have complex multiplication.Modular form 35280.2.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.
