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SageMath
E = EllipticCurve("ez1")
E.isogeny_class()
Elliptic curves in class 20160ez
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
20160.cu2 | 20160ez1 | \([0, 0, 0, -3027, -68416]\) | \(-65743598656/5294205\) | \(-247006428480\) | \([2]\) | \(30720\) | \(0.93250\) | \(\Gamma_0(N)\)-optimal |
20160.cu1 | 20160ez2 | \([0, 0, 0, -49332, -4217344]\) | \(4446542056384/25725\) | \(76814438400\) | \([2]\) | \(61440\) | \(1.2791\) |
Rank
sage: E.rank()
The elliptic curves in class 20160ez have rank \(0\).
Complex multiplication
The elliptic curves in class 20160ez do not have complex multiplication.Modular form 20160.2.a.ez
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.