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SageMath

sage: E = EllipticCurve("86640.d1")

sage: E.isogeny_class()

## Elliptic curves in class 86640.d

sage: E.isogeny_class().curves

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

86640.d1 | 86640bq2 | [0, -1, 0, -21059416, -37190773520] | [2] | 3502080 | |

86640.d2 | 86640bq1 | [0, -1, 0, -1305496, -590710544] | [2] | 1751040 | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 86640.d have rank \(0\).

## Modular form 86640.2.a.d

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.