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SageMath
E = EllipticCurve("br1")
E.isogeny_class()
Elliptic curves in class 38720.br
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 38720.br1 | 38720bs4 | \([0, 0, 0, -458348, 119406672]\) | \(22930509321/6875\) | \(3192778096640000\) | \([2]\) | \(245760\) | \(1.9530\) | |
| 38720.br2 | 38720bs3 | \([0, 0, 0, -226028, -40398512]\) | \(2749884201/73205\) | \(33996701173022720\) | \([2]\) | \(245760\) | \(1.9530\) | |
| 38720.br3 | 38720bs2 | \([0, 0, 0, -32428, 1341648]\) | \(8120601/3025\) | \(1404822362521600\) | \([2, 2]\) | \(122880\) | \(1.6064\) | |
| 38720.br4 | 38720bs1 | \([0, 0, 0, 6292, 149072]\) | \(59319/55\) | \(-25542224773120\) | \([2]\) | \(61440\) | \(1.2599\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 38720.br have rank \(1\).
Complex multiplication
The elliptic curves in class 38720.br do not have complex multiplication.Modular form 38720.2.a.br
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.
