Properties

Label 262080.q
Number of curves 4
Conductor 262080
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("262080.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 262080.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
262080.q1 262080q3 [0, 0, 0, -190627190508, 19913364837077168] [2] 2642411520  
262080.q2 262080q2 [0, 0, 0, -80578750188, -8577163916119888] [2, 2] 1321205760  
262080.q3 262080q1 [0, 0, 0, -80000722668, -8709408057888592] [2] 660602880 \(\Gamma_0(N)\)-optimal
262080.q4 262080q4 [0, 0, 0, 20221249812, -28604067596119888] [2] 2642411520  

Rank

sage: E.rank()
 

The elliptic curves in class 262080.q have rank \(1\).

Modular form 262080.2.a.q

sage: E.q_eigenform(10)
 
\( q - q^{5} - q^{7} - 4q^{11} + q^{13} + 2q^{17} - 8q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.