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SageMath

sage: E = EllipticCurve("1764.f1")

sage: E.isogeny_class()

## Elliptic curves in class 1764.f

sage: E.isogeny_class().curves

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

1764.f1 | 1764a2 | [0, 0, 0, 0, -259308] | [] | 3024 | |

1764.f2 | 1764a1 | [0, 0, 0, 0, 9604] | [3] | 1008 | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 1764.f have rank \(0\).

## Modular form 1764.2.a.f

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

## Isogeny graph

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

The vertices are labelled with LMFDB labels.