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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 489762cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
489762.cw2 | 489762cw1 | \([1, -1, 1, 4531, -520243]\) | \(2924207/34776\) | \(-122367833032536\) | \([]\) | \(1969920\) | \(1.3841\) | \(\Gamma_0(N)\)-optimal* |
489762.cw1 | 489762cw2 | \([1, -1, 1, -41099, 14647169]\) | \(-2181825073/25039686\) | \(-88108238889899046\) | \([]\) | \(5909760\) | \(1.9334\) | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 489762cw have rank \(0\).
Complex multiplication
The elliptic curves in class 489762cw do not have complex multiplication.Modular form 489762.2.a.cw
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.
\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.