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SageMath

sage: E = EllipticCurve("jj1")

sage: E.isogeny_class()

## Elliptic curves in class 193600jj

sage: E.isogeny_class().curves

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

193600.im2 | 193600jj1 | [0, -1, 0, -4033, -384063] | [] | 430080 | \(\Gamma_0(N)\)-optimal |

193600.im1 | 193600jj2 | [0, -1, 0, -5812033, 5395247937] | [] | 4730880 |

## Rank

sage: E.rank()

The elliptic curves in class 193600jj have rank \(0\).

## Complex multiplication

The elliptic curves in class 193600jj do not have complex multiplication.## Modular form 193600.2.a.jj

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

## Isogeny graph

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

The vertices are labelled with Cremona labels.