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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 6384.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 6384.bf1 | 6384k3 | \([0, 1, 0, -1232, -17052]\) | \(202119559492/136857\) | \(140141568\) | \([2]\) | \(4096\) | \(0.50119\) | |
| 6384.bf2 | 6384k2 | \([0, 1, 0, -92, -180]\) | \(340062928/159201\) | \(40755456\) | \([2, 2]\) | \(2048\) | \(0.15462\) | |
| 6384.bf3 | 6384k1 | \([0, 1, 0, -47, 108]\) | \(733001728/10773\) | \(172368\) | \([2]\) | \(1024\) | \(-0.19195\) | \(\Gamma_0(N)\)-optimal |
| 6384.bf4 | 6384k4 | \([0, 1, 0, 328, -1020]\) | \(3799448348/2736741\) | \(-2802422784\) | \([2]\) | \(4096\) | \(0.50119\) |
Rank
sage: E.rank()
The elliptic curves in class 6384.bf have rank \(1\).
Complex multiplication
The elliptic curves in class 6384.bf do not have complex multiplication.Modular form 6384.2.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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
