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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 28560.cw
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 28560.cw1 | 28560dk2 | \([0, 1, 0, -602936, 179775060]\) | \(5918043195362419129/8515734343200\) | \(34880447869747200\) | \([2]\) | \(368640\) | \(2.0767\) | |
| 28560.cw2 | 28560dk1 | \([0, 1, 0, -26936, 4440660]\) | \(-527690404915129/1782829440000\) | \(-7302469386240000\) | \([2]\) | \(184320\) | \(1.7301\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 28560.cw have rank \(0\).
Complex multiplication
The elliptic curves in class 28560.cw do not have complex multiplication.Modular form 28560.2.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 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.
