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SageMath
sage: E = EllipticCurve("eg1")
sage: E.isogeny_class()
Elliptic curves in class 493680.eg
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | Torsion structure | Modular degree | Optimality |
---|---|---|---|---|---|
493680.eg1 | 493680eg2 | [0, 1, 0, -277856, 35917044] | [2] | 5898240 | \(\Gamma_0(N)\)-optimal* |
493680.eg2 | 493680eg1 | [0, 1, 0, 51264, 3926580] | [2] | 2949120 | \(\Gamma_0(N)\)-optimal* |
Rank
sage: E.rank()
The elliptic curves in class 493680.eg have rank \(2\).
Complex multiplication
The elliptic curves in class 493680.eg do not have complex multiplication.Modular form 493680.2.a.eg
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.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.