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SageMath
E = EllipticCurve("en1")
E.isogeny_class()
Elliptic curves in class 424830.en
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
424830.en1 | 424830en2 | \([1, 0, 1, -2890012578, -59788039336952]\) | \(557827933667759/126562500\) | \(605658333770441326560937500\) | \([2]\) | \(499122176\) | \(4.1311\) | \(\Gamma_0(N)\)-optimal* |
424830.en2 | 424830en1 | \([1, 0, 1, -160054998, -1155102416744]\) | \(-94756448879/65610000\) | \(-313973280226596783689190000\) | \([2]\) | \(249561088\) | \(3.7845\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830.en have rank \(0\).
Complex multiplication
The elliptic curves in class 424830.en do not have complex multiplication.Modular form 424830.2.a.en
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.