Properties

Label 19166a
Number of curves 6
Conductor 19166
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("19166.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19166a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19166.a5 19166a1 [1, 0, 0, -713, 14773] [2] 17280 \(\Gamma_0(N)\)-optimal
19166.a4 19166a2 [1, 0, 0, -14403, 663679] [2] 34560  
19166.a6 19166a3 [1, 0, 0, 6132, -309680] [2] 51840  
19166.a3 19166a4 [1, 0, 0, -48628, -3387192] [2] 103680  
19166.a2 19166a5 [1, 0, 0, -233443, -43557759] [2] 155520  
19166.a1 19166a6 [1, 0, 0, -3738083, -2782083455] [2] 311040  

Rank

sage: E.rank()
 

The elliptic curves in class 19166a have rank \(1\).

Modular form 19166.2.a.a

sage: E.q_eigenform(10)
 
\( q + q^{2} - 2q^{3} + q^{4} - 2q^{6} + q^{7} + q^{8} + q^{9} - 2q^{12} + 4q^{13} + q^{14} + q^{16} - 6q^{17} + q^{18} - 2q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.