Properties

Label 54390.cv
Number of curves $6$
Conductor $54390$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("54390.cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54390.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54390.cv1 54390cv4 [1, 0, 0, -16709246, -26290956924] [2] 2654208  
54390.cv2 54390cv6 [1, 0, 0, -14853126, 21936037500] [2] 5308416  
54390.cv3 54390cv3 [1, 0, 0, -1436926, -74580220] [2, 2] 2654208  
54390.cv4 54390cv2 [1, 0, 0, -1044926, -410367420] [2, 2] 1327104  
54390.cv5 54390cv1 [1, 0, 0, -41406, -11167164] [2] 663552 \(\Gamma_0(N)\)-optimal
54390.cv6 54390cv5 [1, 0, 0, 5707274, -593249140] [2] 5308416  

Rank

sage: E.rank()
 

The elliptic curves in class 54390.cv have rank \(1\).

Modular form 54390.2.a.cv

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.