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SageMath
E = EllipticCurve("ey1")
E.isogeny_class()
Elliptic curves in class 422730.ey
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
422730.ey1 | 422730ey2 | \([1, -1, 1, -44690252, 114960047951]\) | \(13540496380264015726564729/5864914552058284800\) | \(4275522708450489619200\) | \([2]\) | \(47185920\) | \(3.1104\) | \(\Gamma_0(N)\)-optimal* |
422730.ey2 | 422730ey1 | \([1, -1, 1, -2354252, 2380156751]\) | \(-1979497032253723108729/2209921299210240000\) | \(-1611032627124264960000\) | \([2]\) | \(23592960\) | \(2.7638\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 422730.ey have rank \(1\).
Complex multiplication
The elliptic curves in class 422730.ey do not have complex multiplication.Modular form 422730.2.a.ey
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.