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SageMath
E = EllipticCurve("w1")
E.isogeny_class()
Elliptic curves in class 5550.w
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5550.w1 | 5550bc3 | \([1, 1, 1, -8011463, -1800202219]\) | \(3639478711331685826729/2016912141902025000\) | \(31514252217219140625000\) | \([2]\) | \(552960\) | \(3.0075\) | |
| 5550.w2 | 5550bc2 | \([1, 1, 1, -4886463, 4131047781]\) | \(825824067562227826729/5613755625000000\) | \(87714931640625000000\) | \([2, 2]\) | \(276480\) | \(2.6609\) | |
| 5550.w3 | 5550bc1 | \([1, 1, 1, -4878463, 4145335781]\) | \(821774646379511057449/38361600000\) | \(599400000000000\) | \([4]\) | \(138240\) | \(2.3144\) | \(\Gamma_0(N)\)-optimal |
| 5550.w4 | 5550bc4 | \([1, 1, 1, -1889463, 9148025781]\) | \(-47744008200656797609/2286529541015625000\) | \(-35727024078369140625000\) | \([2]\) | \(552960\) | \(3.0075\) |
Rank
sage: E.rank()
The elliptic curves in class 5550.w have rank \(1\).
Complex multiplication
The elliptic curves in class 5550.w do not have complex multiplication.Modular form 5550.2.a.w
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.
