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SageMath
E = EllipticCurve("bd1")
E.isogeny_class()
Elliptic curves in class 8550.bd
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 8550.bd1 | 8550bb2 | \([1, -1, 1, -625505, 190568247]\) | \(-2376117230685121/342950\) | \(-3906414843750\) | \([]\) | \(51840\) | \(1.8252\) | |
| 8550.bd2 | 8550bb1 | \([1, -1, 1, -6755, 330747]\) | \(-2992209121/2375000\) | \(-27052734375000\) | \([]\) | \(17280\) | \(1.2759\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 8550.bd have rank \(0\).
Complex multiplication
The elliptic curves in class 8550.bd do not have complex multiplication.Modular form 8550.2.a.bd
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
