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SageMath

sage: E = EllipticCurve("2850.a1")

sage: E.isogeny_class()

## Elliptic curves in class 2850.a

sage: E.isogeny_class().curves

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

2850.a1 | 2850b4 | [1, 1, 0, -76000, 8032750] | [2] | 9216 | |

2850.a2 | 2850b3 | [1, 1, 0, -5500, 81250] | [2] | 9216 | |

2850.a3 | 2850b2 | [1, 1, 0, -4750, 124000] | [2, 2] | 4608 | |

2850.a4 | 2850b1 | [1, 1, 0, -250, 2500] | [2] | 2304 | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 2850.a have rank \(1\).

## Modular form 2850.2.a.a

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.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

## Isogeny graph

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

The vertices are labelled with LMFDB labels.