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SageMath

E = EllipticCurve("j1")

E.isogeny_class()

## Elliptic curves in class 1872.j

sage: E.isogeny_class().curves

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

1872.j1 | 1872c2 | \([0, 0, 0, -615, -5866]\) | \(137842000/117\) | \(21835008\) | \([2]\) | \(512\) | \(0.33544\) | |

1872.j2 | 1872c1 | \([0, 0, 0, -30, -133]\) | \(-256000/507\) | \(-5913648\) | \([2]\) | \(256\) | \(-0.011129\) | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 1872.j have rank \(0\).

## Complex multiplication

The elliptic curves in class 1872.j do not have complex multiplication.## Modular form 1872.2.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.