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SageMath
E = EllipticCurve("bo1")
E.isogeny_class()
Elliptic curves in class 20160.bo
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20160.bo1 | 20160bt4 | \([0, 0, 0, -11664588, 15333885488]\) | \(7347751505995469192/72930375\) | \(1742151462912000\) | \([2]\) | \(491520\) | \(2.5008\) | |
| 20160.bo2 | 20160bt3 | \([0, 0, 0, -1044588, 12537488]\) | \(5276930158229192/3050936350875\) | \(72880377029849088000\) | \([2]\) | \(491520\) | \(2.5008\) | |
| 20160.bo3 | 20160bt2 | \([0, 0, 0, -729588, 239211488]\) | \(14383655824793536/45209390625\) | \(134994517056000000\) | \([2, 2]\) | \(245760\) | \(2.1542\) | |
| 20160.bo4 | 20160bt1 | \([0, 0, 0, -26463, 6898988]\) | \(-43927191786304/415283203125\) | \(-19375453125000000\) | \([2]\) | \(122880\) | \(1.8076\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20160.bo have rank \(1\).
Complex multiplication
The elliptic curves in class 20160.bo do not have complex multiplication.Modular form 20160.2.a.bo
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.
