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SageMath
E = EllipticCurve("bj1")
E.isogeny_class()
Elliptic curves in class 8550.bj
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8550.bj1 | 8550bf3 | \([1, -1, 1, -96305, 11527197]\) | \(8671983378625/82308\) | \(937539562500\) | \([2]\) | \(41472\) | \(1.4595\) | |
| 8550.bj2 | 8550bf4 | \([1, -1, 1, -94055, 12089697]\) | \(-8078253774625/846825858\) | \(-9645875788781250\) | \([2]\) | \(82944\) | \(1.8061\) | |
| 8550.bj3 | 8550bf1 | \([1, -1, 1, -1805, -1803]\) | \(57066625/32832\) | \(373977000000\) | \([2]\) | \(13824\) | \(0.91022\) | \(\Gamma_0(N)\)-optimal |
| 8550.bj4 | 8550bf2 | \([1, -1, 1, 7195, -19803]\) | \(3616805375/2105352\) | \(-23981275125000\) | \([2]\) | \(27648\) | \(1.2568\) |
Rank
sage: E.rank()
The elliptic curves in class 8550.bj have rank \(0\).
Complex multiplication
The elliptic curves in class 8550.bj do not have complex multiplication.Modular form 8550.2.a.bj
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
