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SageMath
E = EllipticCurve("cz1")
E.isogeny_class()
Elliptic curves in class 190608cz
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 190608.l1 | 190608cz1 | \([0, -1, 0, -225384, -41106816]\) | \(26282902468/1881\) | \(90617141412864\) | \([2]\) | \(1290240\) | \(1.7300\) | \(\Gamma_0(N)\)-optimal |
| 190608.l2 | 190608cz2 | \([0, -1, 0, -210944, -46617120]\) | \(-10773969554/3538161\) | \(-340901685995194368\) | \([2]\) | \(2580480\) | \(2.0766\) |
Rank
sage: E.rank()
The elliptic curves in class 190608cz have rank \(2\).
Complex multiplication
The elliptic curves in class 190608cz do not have complex multiplication.Modular form 190608.2.a.cz
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.
