Properties

Label 73920.hc
Number of curves 4
Conductor 73920
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("73920.hc1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 73920.hc

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
73920.hc1 73920dj4 [0, 1, 0, -2111425, 1180177823] [4] 1179648  
73920.hc2 73920dj2 [0, 1, 0, -135745, 17292575] [2, 2] 589824  
73920.hc3 73920dj1 [0, 1, 0, -32065, -1929697] [2] 294912 \(\Gamma_0(N)\)-optimal
73920.hc4 73920dj3 [0, 1, 0, 181055, 86291615] [2] 1179648  

Rank

sage: E.rank()
 

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

Modular form 73920.2.a.hc

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.