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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 60690.bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 60690.bf1 | 60690bf4 | \([1, 0, 1, -107948, 13642076]\) | \(5763259856089/5670\) | \(136860016230\) | \([2]\) | \(294912\) | \(1.4302\) | |
| 60690.bf2 | 60690bf2 | \([1, 0, 1, -6798, 209356]\) | \(1439069689/44100\) | \(1064466792900\) | \([2, 2]\) | \(147456\) | \(1.0836\) | |
| 60690.bf3 | 60690bf1 | \([1, 0, 1, -1018, -7972]\) | \(4826809/1680\) | \(40551115920\) | \([2]\) | \(73728\) | \(0.73704\) | \(\Gamma_0(N)\)-optimal |
| 60690.bf4 | 60690bf3 | \([1, 0, 1, 1872, 708748]\) | \(30080231/9003750\) | \(-217328636883750\) | \([2]\) | \(294912\) | \(1.4302\) |
Rank
sage: E.rank()
The elliptic curves in class 60690.bf have rank \(0\).
Complex multiplication
The elliptic curves in class 60690.bf do not have complex multiplication.Modular form 60690.2.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.
