Properties

Label 73920ew
Number of curves $6$
Conductor $73920$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("73920.bv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 73920ew

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
73920.bv4 73920ew1 [0, -1, 0, -16961, -844575] [2] 131072 \(\Gamma_0(N)\)-optimal
73920.bv3 73920ew2 [0, -1, 0, -17281, -810719] [2, 2] 262144  
73920.bv5 73920ew3 [0, -1, 0, 16319, -3612959] [2] 524288  
73920.bv2 73920ew4 [0, -1, 0, -56001, 4153185] [2, 2] 524288  
73920.bv6 73920ew5 [0, -1, 0, 116479, 24540321] [2] 1048576  
73920.bv1 73920ew6 [0, -1, 0, -848001, 300836385] [2] 1048576  

Rank

sage: E.rank()
 

The elliptic curves in class 73920ew have rank \(2\).

Modular form 73920.2.a.bv

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{7} + q^{9} + q^{11} + 2q^{13} + q^{15} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.