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SageMath

sage: E = EllipticCurve("s1")

sage: E.isogeny_class()

## Elliptic curves in class 17424.s

sage: E.isogeny_class().curves

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

17424.s1 | 17424bu2 | [0, 0, 0, -43923, 13850386] | [] | 101376 | |

17424.s2 | 17424bu1 | [0, 0, 0, -4323, -109406] | [] | 9216 | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 17424.s have rank \(0\).

## Complex multiplication

The elliptic curves in class 17424.s do not have complex multiplication.## Modular form 17424.2.a.s

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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.