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SageMath

sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 3360.j

sage: E.isogeny_class().curves

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

3360.j1 | 3360h1 | \([0, -1, 0, -210, -900]\) | \(16079333824/2953125\) | \(189000000\) | \([2]\) | \(1152\) | \(0.30659\) | \(\Gamma_0(N)\)-optimal |

3360.j2 | 3360h2 | \([0, -1, 0, 415, -5775]\) | \(1925134784/4465125\) | \(-18289152000\) | \([2]\) | \(2304\) | \(0.65316\) |

## Rank

sage: E.rank()

The elliptic curves in class 3360.j have rank \(1\).

## Complex multiplication

The elliptic curves in class 3360.j do not have complex multiplication.## Modular form 3360.2.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 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.