Properties

Label 19110.cv
Number of curves $6$
Conductor $19110$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("19110.cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 19110.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
19110.cv1 19110cn5 [1, 0, 0, -441736, 112966790] [2] 196608  
19110.cv2 19110cn3 [1, 0, 0, -41406, -3243864] [2] 98304  
19110.cv3 19110cn4 [1, 0, 0, -27686, 1752960] [2, 2] 98304  
19110.cv4 19110cn6 [1, 0, 0, -5636, 4473930] [2] 196608  
19110.cv5 19110cn2 [1, 0, 0, -3186, -25740] [2, 2] 49152  
19110.cv6 19110cn1 [1, 0, 0, 734, -3004] [2] 24576 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 19110.cv have rank \(0\).

Modular form 19110.2.a.cv

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{3} + q^{4} - q^{5} + q^{6} + q^{8} + q^{9} - q^{10} + 4q^{11} + q^{12} - q^{13} - q^{15} + q^{16} + 6q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.