Properties

Label 17640.bq
Number of curves 4
Conductor 17640
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("17640.bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 17640.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
17640.bq1 17640cs3 [0, 0, 0, -47187, -3945186] [2] 36864  
17640.bq2 17640cs2 [0, 0, 0, -3087, -55566] [2, 2] 18432  
17640.bq3 17640cs1 [0, 0, 0, -882, 9261] [2] 9216 \(\Gamma_0(N)\)-optimal
17640.bq4 17640cs4 [0, 0, 0, 5733, -314874] [2] 36864  

Rank

sage: E.rank()
 

The elliptic curves in class 17640.bq have rank \(1\).

Modular form 17640.2.a.bq

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

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.