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SageMath

sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 424830.g

sage: E.isogeny_class().curves

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

424830.g1 | 424830g2 | \([1, 1, 0, -768023, 258745677]\) | \(-12242088317612041/600\) | \(-2455517400\) | \([]\) | \(2939328\) | \(1.7255\) |
\(\Gamma_0(N)\)-optimal^{*} |

424830.g2 | 424830g1 | \([1, 1, 0, -9398, 358002]\) | \(-22434194041/843750\) | \(-3453071343750\) | \([]\) | \(979776\) | \(1.1762\) |
\(\Gamma_0(N)\)-optimal^{*} |

^{*}optimality has not been determined rigorously for conductors over 400000. In this case the optimal curve is certainly one of the 2 curves highlighted, and conditionally curve 424830.g1.

## Rank

sage: E.rank()

The elliptic curves in class 424830.g have rank \(1\).

## Complex multiplication

The elliptic curves in class 424830.g do not have complex multiplication.## Modular form 424830.2.a.g

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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.