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SageMath

sage: E = EllipticCurve("bn1")

sage: E.isogeny_class()

## Elliptic curves in class 17640.bn

sage: E.isogeny_class().curves

LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|

17640.bn1 | 17640bh2 | \([0, 0, 0, -105987, 9445534]\) | \(2185454/625\) | \(37654757763840000\) | \([2]\) | \(129024\) | \(1.8872\) | |

17640.bn2 | 17640bh1 | \([0, 0, 0, 17493, 974806]\) | \(19652/25\) | \(-753095155276800\) | \([2]\) | \(64512\) | \(1.5406\) | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 17640.bn have rank \(0\).

## Complex multiplication

The elliptic curves in class 17640.bn do not have complex multiplication.## Modular form 17640.2.a.bn

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.