Properties

Label 243600.cv
Number of curves $6$
Conductor $243600$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("243600.cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 243600.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
243600.cv1 243600cv4 [0, -1, 0, -81849608, -284991198288] [2] 12582912  
243600.cv2 243600cv5 [0, -1, 0, -16987608, 21913217712] [2] 25165824  
243600.cv3 243600cv3 [0, -1, 0, -5213608, -4272158288] [2, 2] 12582912  
243600.cv4 243600cv2 [0, -1, 0, -5115608, -4451694288] [2, 2] 6291456  
243600.cv5 243600cv1 [0, -1, 0, -313608, -72270288] [2] 3145728 \(\Gamma_0(N)\)-optimal
243600.cv6 243600cv6 [0, -1, 0, 4992392, -18968798288] [2] 25165824  

Rank

sage: E.rank()
 

The elliptic curves in class 243600.cv have rank \(0\).

Modular form 243600.2.a.cv

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{7} + q^{9} - 4q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.