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SageMath
sage: E = EllipticCurve("bb1")
sage: E.isogeny_class()
Elliptic curves in class 424830bb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
424830.bb2 | 424830bb1 | [1, 1, 0, -105040258628, 13161979018702032] | [2] | 3609722880 | \(\Gamma_0(N)\)-optimal* |
424830.bb1 | 424830bb2 | [1, 1, 0, -1682734261828, 840177500560518352] | [2] | 7219445760 | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 424830bb have rank \(0\).
Complex multiplication
The elliptic curves in class 424830bb do not have complex multiplication.Modular form 424830.2.a.bb
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.