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SageMath

sage: E = EllipticCurve("n1")

sage: E.isogeny_class()

## Elliptic curves in class 1152.n

sage: E.isogeny_class().curves

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

1152.n1 | 1152a2 | \([0, 0, 0, -24, 32]\) | \(3456\) | \(442368\) | \([2]\) | \(128\) | \(-0.21042\) | |

1152.n2 | 1152a1 | \([0, 0, 0, -9, -10]\) | \(23328\) | \(3456\) | \([2]\) | \(64\) | \(-0.55700\) | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 1152.n have rank \(1\).

## Complex multiplication

The elliptic curves in class 1152.n do not have complex multiplication.## Modular form 1152.2.a.n

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.