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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 5850.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 5850.bf1 | 5850bw1 | \([1, -1, 1, -82046255, 286066759047]\) | \(-134057911417971280740025/1872\) | \(-852930000\) | \([]\) | \(268800\) | \(2.6933\) | \(\Gamma_0(N)\)-optimal |
| 5850.bf2 | 5850bw2 | \([1, -1, 1, -79943180, 301424274447]\) | \(-198417696411528597145/22989483914821632\) | \(-6546614755431628800000000\) | \([]\) | \(1344000\) | \(3.4980\) |
Rank
sage: E.rank()
The elliptic curves in class 5850.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 5850.bf do not have complex multiplication.Modular form 5850.2.a.bf
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.
\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
