Properties

Label 209484.bq
Number of curves 2
Conductor 209484
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("209484.bq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 209484.bq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
209484.bq1 209484be2 [0, 0, 0, -58719, -2603738] [2] 1216512  
209484.bq2 209484be1 [0, 0, 0, 12696, -304175] [2] 608256 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 209484.bq have rank \(1\).

Modular form 209484.2.a.bq

sage: E.q_eigenform(10)
 
\( q + 2q^{5} + 2q^{7} + q^{11} - 2q^{13} + 4q^{17} + 6q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.