Properties

Label 262086cw
Number of curves $4$
Conductor $262086$
CM no
Rank $0$
Graph

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Show commands: 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)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + 4 q^{7} + q^{8} + q^{9} - q^{12} - 4 q^{13} + 4 q^{14} + q^{16} - 6 q^{17} + q^{18} + O(q^{20})\) Copy content Toggle raw display

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.