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SageMath

sage: E = EllipticCurve("by1")

sage: E.isogeny_class()

## Elliptic curves in class 62400by

sage: E.isogeny_class().curves

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

62400.h2 | 62400by1 | [0, -1, 0, -14236833, -20671178463] | [2] | 2949120 | \(\Gamma_0(N)\)-optimal |

62400.h1 | 62400by2 | [0, -1, 0, -14556833, -19692938463] | [2] | 5898240 |

## Rank

sage: E.rank()

The elliptic curves in class 62400by have rank \(1\).

## Complex multiplication

The elliptic curves in class 62400by do not have complex multiplication.## Modular form 62400.2.a.by

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.