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SageMath
E = EllipticCurve("cw1")
E.isogeny_class()
Elliptic curves in class 262086cw
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
262086.cw3 | 262086cw1 | \([1, 1, 1, -350358, 5950803]\) | \(57066625/32832\) | \(2736371482815592512\) | \([2]\) | \(6220800\) | \(2.2274\) | \(\Gamma_0(N)\)-optimal |
262086.cw4 | 262086cw2 | \([1, 1, 1, 1396882, 49282355]\) | \(3616805375/2105352\) | \(-175469821335549869832\) | \([2]\) | \(12441600\) | \(2.5739\) | |
262086.cw1 | 262086cw3 | \([1, 1, 1, -18696378, -31123575933]\) | \(8671983378625/82308\) | \(6859931286780756228\) | \([2]\) | \(18662400\) | \(2.7767\) | |
262086.cw2 | 262086cw4 | \([1, 1, 1, -18259568, -32646470317]\) | \(-8078253774625/846825858\) | \(-70578403044043810451778\) | \([2]\) | \(37324800\) | \(3.1232\) |
Rank
sage: E.rank()
The elliptic curves in class 262086cw have rank \(0\).
Complex multiplication
The elliptic curves in class 262086cw do not have complex multiplication.Modular form 262086.2.a.cw
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.
\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with Cremona labels.