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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 48510cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 48510.cj4 | 48510cs1 | \([1, -1, 1, 113107, 19464981]\) | \(1865864036231/2993760000\) | \(-256763182404960000\) | \([2]\) | \(491520\) | \(2.0257\) | \(\Gamma_0(N)\)-optimal |
| 48510.cj3 | 48510cs2 | \([1, -1, 1, -768893, 199040181]\) | \(586145095611769/140040608400\) | \(12010739764948016400\) | \([2, 2]\) | \(983040\) | \(2.3723\) | |
| 48510.cj2 | 48510cs3 | \([1, -1, 1, -4164593, -3102938499]\) | \(93137706732176569/5369647977540\) | \(460533878169100922340\) | \([2]\) | \(1966080\) | \(2.7189\) | |
| 48510.cj1 | 48510cs4 | \([1, -1, 1, -11485193, 14983247661]\) | \(1953542217204454969/170843779260\) | \(14652608244110450460\) | \([2]\) | \(1966080\) | \(2.7189\) |
Rank
sage: E.rank()
The elliptic curves in class 48510cs have rank \(0\).
Complex multiplication
The elliptic curves in class 48510cs do not have complex multiplication.Modular form 48510.2.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 Cremona 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 Cremona labels.
