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SageMath

sage: E = EllipticCurve("h1")

sage: E.isogeny_class()

## Elliptic curves in class 93600h

sage: E.isogeny_class().curves

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

93600.n2 | 93600h1 | \([0, 0, 0, 675, 121500]\) | \(1728/325\) | \(-6396975000000\) | \([2]\) | \(147456\) | \(1.1365\) | \(\Gamma_0(N)\)-optimal |

93600.n1 | 93600h2 | \([0, 0, 0, -33075, 2247750]\) | \(25412184/845\) | \(133057080000000\) | \([2]\) | \(294912\) | \(1.4831\) |

## Rank

sage: E.rank()

The elliptic curves in class 93600h have rank \(0\).

## Complex multiplication

The elliptic curves in class 93600h do not have complex multiplication.## Modular form 93600.2.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.