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SageMath

sage: E = EllipticCurve("108900.x1")

sage: E.isogeny_class()

## Elliptic curves in class 108900.x

sage: E.isogeny_class().curves

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

108900.x1 | 108900cf2 | [0, 0, 0, -335775, -35604250] | [2] | 1474560 | |

108900.x2 | 108900cf1 | [0, 0, 0, 72600, -4159375] | [2] | 737280 | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 108900.x have rank \(2\).

## Modular form 108900.2.a.x

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.