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SageMath

sage: E = EllipticCurve("16830.b1")

sage: E.isogeny_class()

## Elliptic curves in class 16830s

sage: E.isogeny_class().curves

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

16830.b2 | 16830s1 | [1, -1, 0, 14355, -675675] | [2] | 86016 | \(\Gamma_0(N)\)-optimal |

16830.b1 | 16830s2 | [1, -1, 0, -83565, -6374619] | [2] | 172032 |

## Rank

sage: E.rank()

The elliptic curves in class 16830s have rank \(1\).

## Modular form 16830.2.a.b

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.