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SageMath

sage: E = EllipticCurve("fl1")

sage: E.isogeny_class()

## Elliptic curves in class 224400.fl

sage: E.isogeny_class().curves

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

224400.fl1 | 224400bt1 | [0, 1, 0, -78408, 8419188] | [2] | 737280 | \(\Gamma_0(N)\)-optimal |

224400.fl2 | 224400bt2 | [0, 1, 0, -62408, 11971188] | [2] | 1474560 |

## Rank

sage: E.rank()

The elliptic curves in class 224400.fl have rank \(2\).

## Complex multiplication

The elliptic curves in class 224400.fl do not have complex multiplication.## Modular form 224400.2.a.fl

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.