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SageMath
sage: E = EllipticCurve("cc1")
sage: E.isogeny_class()
Elliptic curves in class 44880cc
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
44880.cc2 | 44880cc1 | [0, 1, 0, 424, -2796] | [2] | 24576 | \(\Gamma_0(N)\)-optimal |
44880.cc1 | 44880cc2 | [0, 1, 0, -2296, -27820] | [2] | 49152 |
Rank
sage: E.rank()
The elliptic curves in class 44880cc have rank \(0\).
Complex multiplication
The elliptic curves in class 44880cc do not have complex multiplication.Modular form 44880.2.a.cc
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 Cremona 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 Cremona labels.