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SageMath
E = EllipticCurve("r1")
E.isogeny_class()
Elliptic curves in class 9576.r
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9576.r1 | 9576n2 | \([0, 0, 0, -56619, 5185350]\) | \(497953800342/17689\) | \(713057458176\) | \([2]\) | \(24576\) | \(1.3638\) | |
| 9576.r2 | 9576n1 | \([0, 0, 0, -3699, 73278]\) | \(277706124/45619\) | \(919468827648\) | \([2]\) | \(12288\) | \(1.0172\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 9576.r have rank \(0\).
Complex multiplication
The elliptic curves in class 9576.r do not have complex multiplication.Modular form 9576.2.a.r
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.
