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SageMath
E = EllipticCurve("cs1")
E.isogeny_class()
Elliptic curves in class 47040.cs
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 47040.cs1 | 47040fb4 | \([0, -1, 0, -352865, -80555775]\) | \(157551496201/13125\) | \(404787855360000\) | \([2]\) | \(393216\) | \(1.8467\) | |
| 47040.cs2 | 47040fb2 | \([0, -1, 0, -23585, -1067583]\) | \(47045881/11025\) | \(340021798502400\) | \([2, 2]\) | \(196608\) | \(1.5001\) | |
| 47040.cs3 | 47040fb1 | \([0, -1, 0, -7905, 258945]\) | \(1771561/105\) | \(3238302842880\) | \([2]\) | \(98304\) | \(1.1536\) | \(\Gamma_0(N)\)-optimal |
| 47040.cs4 | 47040fb3 | \([0, -1, 0, 54815, -6728063]\) | \(590589719/972405\) | \(-29989922627911680\) | \([2]\) | \(393216\) | \(1.8467\) |
Rank
sage: E.rank()
The elliptic curves in class 47040.cs have rank \(0\).
Complex multiplication
The elliptic curves in class 47040.cs do not have complex multiplication.Modular form 47040.2.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.
