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SageMath
E = EllipticCurve("x1")
E.isogeny_class()
Elliptic curves in class 20592.x
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 20592.x1 | 20592bq2 | \([0, 0, 0, -1875, 23506]\) | \(244140625/61347\) | \(183181160448\) | \([2]\) | \(16384\) | \(0.87109\) | |
| 20592.x2 | 20592bq1 | \([0, 0, 0, 285, 2338]\) | \(857375/1287\) | \(-3842961408\) | \([2]\) | \(8192\) | \(0.52452\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 20592.x have rank \(1\).
Complex multiplication
The elliptic curves in class 20592.x do not have complex multiplication.Modular form 20592.2.a.x
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.
