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SageMath

sage: E = EllipticCurve("33640.h1")

sage: E.isogeny_class()

## Elliptic curves in class 33640b

sage: E.isogeny_class().curves

LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|

33640.h2 | 33640b1 | [0, -1, 0, -211371, -37153480] | [2] | 259840 | \(\Gamma_0(N)\)-optimal |

33640.h1 | 33640b2 | [0, -1, 0, -333316, 10746516] | [2] | 519680 |

## Rank

sage: E.rank()

The elliptic curves in class 33640b have rank \(0\).

## Modular form 33640.2.a.h

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.