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SageMath
E = EllipticCurve("cb1")
E.isogeny_class()
Elliptic curves in class 41280cb
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
41280.a1 | 41280cb1 | \([0, -1, 0, -1441, -20159]\) | \(1263214441/29025\) | \(7608729600\) | \([2]\) | \(36864\) | \(0.68237\) | \(\Gamma_0(N)\)-optimal |
41280.a2 | 41280cb2 | \([0, -1, 0, 159, -63999]\) | \(1685159/6739605\) | \(-1766747013120\) | \([2]\) | \(73728\) | \(1.0289\) |
Rank
sage: E.rank()
The elliptic curves in class 41280cb have rank \(2\).
Complex multiplication
The elliptic curves in class 41280cb do not have complex multiplication.Modular form 41280.2.a.cb
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.