Properties

Label 92400.cv
Number of curves 6
Conductor 92400
CM no
Rank 2
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("92400.cv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 92400.cv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
92400.cv1 92400ev6 [0, -1, 0, -1807608, 936017712] [2] 1310720  
92400.cv2 92400ev4 [0, -1, 0, -113608, 14481712] [2, 2] 655360  
92400.cv3 92400ev2 [0, -1, 0, -15608, -414288] [2, 2] 327680  
92400.cv4 92400ev1 [0, -1, 0, -13608, -606288] [2] 163840 \(\Gamma_0(N)\)-optimal
92400.cv5 92400ev5 [0, -1, 0, 12392, 44721712] [2] 1310720  
92400.cv6 92400ev3 [0, -1, 0, 50392, -3054288] [2] 655360  

Rank

sage: E.rank()
 

The elliptic curves in class 92400.cv have rank \(2\).

Modular form 92400.2.a.cv

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{7} + q^{9} + q^{11} - 6q^{13} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.