Properties

Label 73920.eq
Number of curves $6$
Conductor $73920$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("73920.eq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 73920.eq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
73920.eq1 73920ca6 [0, 1, 0, -848001, -300836385] [2] 1048576  
73920.eq2 73920ca4 [0, 1, 0, -56001, -4153185] [2, 2] 524288  
73920.eq3 73920ca2 [0, 1, 0, -17281, 810719] [2, 2] 262144  
73920.eq4 73920ca1 [0, 1, 0, -16961, 844575] [2] 131072 \(\Gamma_0(N)\)-optimal
73920.eq5 73920ca3 [0, 1, 0, 16319, 3612959] [2] 524288  
73920.eq6 73920ca5 [0, 1, 0, 116479, -24540321] [2] 1048576  

Rank

sage: E.rank()
 

The elliptic curves in class 73920.eq have rank \(0\).

Modular form 73920.2.a.eq

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 LMFDB numbering.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.