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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 166464cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 166464.hh1 | 166464cw1 | \([0, 0, 0, -419628, 66423760]\) | \(1771561/612\) | \(2823009896814870528\) | \([2]\) | \(3538944\) | \(2.2421\) | \(\Gamma_0(N)\)-optimal |
| 166464.hh2 | 166464cw2 | \([0, 0, 0, 1245012, 462608080]\) | \(46268279/46818\) | \(-215960257106337595392\) | \([2]\) | \(7077888\) | \(2.5887\) |
Rank
sage: E.rank()
The elliptic curves in class 166464cw have rank \(1\).
Complex multiplication
The elliptic curves in class 166464cw do not have complex multiplication.Modular form 166464.2.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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.
