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SageMath

sage: E = EllipticCurve("286650.x1")

sage: E.isogeny_class()

## Elliptic curves in class 286650.x

sage: E.isogeny_class().curves

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

286650.x1 | 286650x2 | [1, -1, 0, -9399042, -11088687884] | [2] | 11059200 | |

286650.x2 | 286650x1 | [1, -1, 0, -579042, -178347884] | [2] | 5529600 | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 286650.x have rank \(1\).

## Modular form 286650.2.a.x

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.