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SageMath

sage: E = EllipticCurve("d1")

sage: E.isogeny_class()

## Elliptic curves in class 1950.d

sage: E.isogeny_class().curves

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

1950.d1 | 1950d2 | \([1, 1, 0, -88075, 9992125]\) | \(38686490446661/141927552\) | \(277202250000000\) | \([2]\) | \(17920\) | \(1.6317\) | |

1950.d2 | 1950d1 | \([1, 1, 0, -8075, -7875]\) | \(29819839301/17252352\) | \(33696000000000\) | \([2]\) | \(8960\) | \(1.2852\) | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 1950.d have rank \(0\).

## Complex multiplication

The elliptic curves in class 1950.d do not have complex multiplication.## Modular form 1950.2.a.d

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.