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SageMath
sage: E = EllipticCurve("k1")
sage: E.isogeny_class()
Elliptic curves in class 1650.k
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
1650.k1 | 1650f3 | [1, 0, 1, -8801, -318502] | [2] | 2048 | |
1650.k2 | 1650f2 | [1, 0, 1, -551, -5002] | [2, 2] | 1024 | |
1650.k3 | 1650f4 | [1, 0, 1, -301, -9502] | [2] | 2048 | |
1650.k4 | 1650f1 | [1, 0, 1, -51, -2] | [2] | 512 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 1650.k have rank \(0\).
Complex multiplication
The elliptic curves in class 1650.k do not have complex multiplication.Modular form 1650.2.a.k
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.