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SageMath

sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 3600.n

sage: E.isogeny_class().curves

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

3600.n1 | 3600u2 | [0, 0, 0, -1515, -14150] | [2] | 3072 | |

3600.n2 | 3600u1 | [0, 0, 0, 285, -1550] | [2] | 1536 | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 3600.n have rank \(1\).

## Complex multiplication

The elliptic curves in class 3600.n do not have complex multiplication.## Modular form 3600.2.a.n

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.