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SageMath
sage: E = EllipticCurve("o1")
sage: E.isogeny_class()
Elliptic curves in class 185020.o
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
185020.o1 | 185020m4 | [0, -1, 0, -5971380, -5614436728] | [2] | 5225472 | |
185020.o2 | 185020m3 | [0, -1, 0, -374525, -86982730] | [2] | 2612736 | |
185020.o3 | 185020m2 | [0, -1, 0, -84380, -5303128] | [2] | 1741824 | |
185020.o4 | 185020m1 | [0, -1, 0, -38125, 2819250] | [2] | 870912 | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 185020.o have rank \(2\).
Complex multiplication
The elliptic curves in class 185020.o do not have complex multiplication.Modular form 185020.2.a.o
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.