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SageMath
E = EllipticCurve("bg1")
E.isogeny_class()
Elliptic curves in class 9600.bg
sage: E.isogeny_class().curves
| LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
|---|---|---|---|---|---|---|---|---|
| 9600.bg1 | 9600t1 | \([0, 1, 0, -208258, 36511238]\) | \(499460194376672/253125\) | \(506250000000\) | \([2]\) | \(46080\) | \(1.5787\) | \(\Gamma_0(N)\)-optimal |
| 9600.bg2 | 9600t2 | \([0, 1, 0, -207133, 36926363]\) | \(-3839138053504/87890625\) | \(-22500000000000000\) | \([2]\) | \(92160\) | \(1.9253\) |
Rank
sage: E.rank()
The elliptic curves in class 9600.bg have rank \(0\).
Complex multiplication
The elliptic curves in class 9600.bg do not have complex multiplication.Modular form 9600.2.a.bg
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.
