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SageMath
sage: E = EllipticCurve("f1")
sage: E.isogeny_class()
Elliptic curves in class 41650.f
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
41650.f1 | 41650n4 | [1, 0, 1, -138451, 13690548] | [2] | 497664 | |
41650.f2 | 41650n3 | [1, 0, 1, -126201, 17243048] | [2] | 248832 | |
41650.f3 | 41650n2 | [1, 0, 1, -52701, -4659952] | [2] | 165888 | |
41650.f4 | 41650n1 | [1, 0, 1, -3701, -53952] | [2] | 82944 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 41650.f have rank \(0\).
Complex multiplication
The elliptic curves in class 41650.f do not have complex multiplication.Modular form 41650.2.a.f
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.