Properties

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

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

Elliptic curves in class 17640.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
17640.bq1 17640cs3 \([0, 0, 0, -47187, -3945186]\) \(132304644/5\) \(439122539520\) \([2]\) \(36864\) \(1.3200\)  
17640.bq2 17640cs2 \([0, 0, 0, -3087, -55566]\) \(148176/25\) \(548903174400\) \([2, 2]\) \(18432\) \(0.97347\)  
17640.bq3 17640cs1 \([0, 0, 0, -882, 9261]\) \(55296/5\) \(6861289680\) \([2]\) \(9216\) \(0.62690\) \(\Gamma_0(N)\)-optimal
17640.bq4 17640cs4 \([0, 0, 0, 5733, -314874]\) \(237276/625\) \(-54890317440000\) \([2]\) \(36864\) \(1.3200\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 17640.bq do not have complex multiplication.

Modular form 17640.2.a.bq

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