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SageMath

sage: E = EllipticCurve("hp1")

sage: E.isogeny_class()

## Elliptic curves in class 193600.hp

sage: E.isogeny_class().curves

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

193600.hp1 | 193600jd2 | [0, -1, 0, -488033, 513139937] | [] | 4730880 | |

193600.hp2 | 193600jd1 | [0, -1, 0, -48033, -4036063] | [] | 430080 | \(\Gamma_0(N)\)-optimal |

## Rank

sage: E.rank()

The elliptic curves in class 193600.hp have rank \(0\).

## Complex multiplication

The elliptic curves in class 193600.hp do not have complex multiplication.## Modular form 193600.2.a.hp

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.

\(\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)\)

## Isogeny graph

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

The vertices are labelled with LMFDB labels.