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SageMath
E = EllipticCurve("bf1")
E.isogeny_class()
Elliptic curves in class 190608bf
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190608.b1 | 190608bf1 | \([0, -1, 0, -7407840, 7761067776]\) | \(233301213501481/63562752\) | \(12248537770494001152\) | \([2]\) | \(8294400\) | \(2.6455\) | \(\Gamma_0(N)\)-optimal |
| 190608.b2 | 190608bf2 | \([0, -1, 0, -6483680, 9768343296]\) | \(-156425280396841/123297834528\) | \(-23759483907121066672128\) | \([2]\) | \(16588800\) | \(2.9921\) |
Rank
sage: E.rank()
The elliptic curves in class 190608bf have rank \(1\).
Complex multiplication
The elliptic curves in class 190608bf do not have complex multiplication.Modular form 190608.2.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 Cremona numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
