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SageMath
sage: E = EllipticCurve("bk1")
sage: E.isogeny_class()
Elliptic curves in class 11200.bk
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
11200.bk1 | 11200bv3 | [0, 0, 0, -29900, -1990000] | [2] | 16384 | |
11200.bk2 | 11200bv4 | [0, 0, 0, -5900, 138000] | [2] | 16384 | |
11200.bk3 | 11200bv2 | [0, 0, 0, -1900, -30000] | [2, 2] | 8192 | |
11200.bk4 | 11200bv1 | [0, 0, 0, 100, -2000] | [2] | 4096 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 11200.bk have rank \(0\).
Complex multiplication
The elliptic curves in class 11200.bk do not have complex multiplication.Modular form 11200.2.a.bk
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.
\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.