Show commands:
SageMath

sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 435344.j

sage: E.isogeny_class().curves

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

435344.j1 | 435344j2 | \([0, 1, 0, -1637328, -755502188]\) | \(24553362849625/1755162752\) | \(34700637666584035328\) | \([2]\) | \(12644352\) | \(2.4964\) |
\(\Gamma_0(N)\)-optimal^{*} |

435344.j2 | 435344j1 | \([0, 1, 0, 93232, -51510380]\) | \(4533086375/60669952\) | \(-1199481939325616128\) | \([2]\) | \(6322176\) | \(2.1498\) |
\(\Gamma_0(N)\)-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 435344.j1.

## Rank

sage: E.rank()

The elliptic curves in class 435344.j have rank \(0\).

## Complex multiplication

The elliptic curves in class 435344.j do not have complex multiplication.## Modular form 435344.2.a.j

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

## Isogeny graph

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

The vertices are labelled with LMFDB labels.