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SageMath

sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 2760j

sage: E.isogeny_class().curves

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

2760.k2 | 2760j1 | \([0, 1, 0, -32040, 2291328]\) | \(-3552342505518244/179863605135\) | \(-184180331658240\) | \([2]\) | \(10560\) | \(1.4978\) | \(\Gamma_0(N)\)-optimal |

2760.k1 | 2760j2 | \([0, 1, 0, -518720, 143623200]\) | \(7536914291382802562/17961229575\) | \(36784598169600\) | \([2]\) | \(21120\) | \(1.8444\) |

## Rank

sage: E.rank()

The elliptic curves in class 2760j have rank \(0\).

## Complex multiplication

The elliptic curves in class 2760j do not have complex multiplication.## Modular form 2760.2.a.j

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.