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SageMath

sage: E = EllipticCurve("24048.c1")

sage: E.isogeny_class()

sage: E.isogeny_class()

## Elliptic curves in class 24048i

sage: E.isogeny_class().curves

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

24048.c2 | 24048i1 | [0, 0, 0, -651, -26566] | 2 | 27648 | \(\Gamma_0(N)\)-optimal |

24048.c1 | 24048i2 | [0, 0, 0, -17931, -921670] | 2 | 55296 |

## Rank

sage: E.rank()

The elliptic curves in class 24048i 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.