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SageMath

sage: E = EllipticCurve("363726.j1")

sage: E.isogeny_class()

sage: E.isogeny_class()

## Elliptic curves in class 363726j

sage: E.isogeny_class().curves

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

363726.j2 | 363726j1 | [1, -1, 0, -4923, -551259] | 2 | 1474560 | \(\Gamma_0(N)\)-optimal^{*} |

363726.j1 | 363726j2 | [1, -1, 0, -135603, -19133955] | 2 | 2949120 | \(\Gamma_0(N)\)-optimal^{*} |

^{*}optimality has not been proved rigorously for conductors over 270000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 363726j1.

## Rank

sage: E.rank()

The elliptic curves in class 363726j have rank \(0\).

## Modular form None

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.