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SageMath

sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 424830.bc

sage: E.isogeny_class().curves

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

424830.bc1 | 424830bc2 | [1, 1, 0, -1735017, -1383719931] | [] | 26873856 | |

424830.bc2 | 424830bc1 | [1, 1, 0, 176718, 31346316] | [] | 8957952 |
\(\Gamma_0(N)\)-optimal^{*} |

^{*}optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 0 curves highlighted, and conditionally curve 424830.bc1.

## Rank

sage: E.rank()

The elliptic curves in class 424830.bc have rank \(0\).

## Complex multiplication

The elliptic curves in class 424830.bc do not have complex multiplication.## Modular form 424830.2.a.bc

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

## Isogeny graph

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

The vertices are labelled with LMFDB labels.