Show commands for:
SageMath

sage: E = EllipticCurve("108.a1")

sage: E.isogeny_class()

sage: E.isogeny_class()

## Elliptic curves in class 108a

sage: E.isogeny_class().curves

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

108.a2 | 108a1 | [0, 0, 0, 0, 4] | 3 | 6 | \(\Gamma_0(N)\)-optimal |

108.a1 | 108a2 | [0, 0, 0, 0, -108] | 1 | 18 |

## Rank

sage: E.rank()

The elliptic curves in class 108a have rank \(0\).

## Modular form 108.2.a.a

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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels.