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SageMath

sage: E = EllipticCurve("86640.ch1")

sage: E.isogeny_class()

## Elliptic curves in class 86640.ch

sage: E.isogeny_class().curves

LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|

86640.ch1 | 86640cy2 | [0, 1, 0, -58336, 5403764] | [2] | 184320 | |

86640.ch2 | 86640cy1 | [0, 1, 0, -3616, 84980] | [2] | 92160 | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 86640.ch have rank \(1\).

## Modular form 86640.2.a.ch

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels.