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SageMath

sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 3528q

sage: E.isogeny_class().curves

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

3528.e2 | 3528q1 | [0, 0, 0, -2646, 83349] | [2] | 4608 | \(\Gamma_0(N)\)-optimal |

3528.e1 | 3528q2 | [0, 0, 0, -48951, 4167450] | [2] | 9216 |

## Rank

sage: E.rank()

The elliptic curves in class 3528q have rank \(1\).

## Complex multiplication

The elliptic curves in class 3528q do not have complex multiplication.## Modular form 3528.2.a.q

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 Cremona 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 Cremona labels.