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SageMath

sage: E = EllipticCurve("cp1")

sage: E.isogeny_class()

## Elliptic curves in class 92400.cp

sage: E.isogeny_class().curves

LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|

92400.cp1 | 92400bm2 | \([0, -1, 0, -448, 2992]\) | \(77860436/17787\) | \(2276736000\) | \([2]\) | \(36864\) | \(0.50799\) | |

92400.cp2 | 92400bm1 | \([0, -1, 0, -148, -608]\) | \(11279504/693\) | \(22176000\) | \([2]\) | \(18432\) | \(0.16142\) | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 92400.cp have rank \(1\).

## Complex multiplication

The elliptic curves in class 92400.cp do not have complex multiplication.## Modular form 92400.2.a.cp

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.