Properties

Label 20160fg
Number of curves $6$
Conductor $20160$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("20160.fg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 20160fg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
20160.fg4 20160fg1 [0, 0, 0, -6312, 193016] [2] 16384 \(\Gamma_0(N)\)-optimal
20160.fg3 20160fg2 [0, 0, 0, -6492, 181424] [2, 2] 32768  
20160.fg2 20160fg3 [0, 0, 0, -24492, -1280176] [2, 2] 65536  
20160.fg5 20160fg4 [0, 0, 0, 8628, 901136] [2] 65536  
20160.fg1 20160fg5 [0, 0, 0, -377292, -89197936] [2] 131072  
20160.fg6 20160fg6 [0, 0, 0, 40308, -6904816] [2] 131072  

Rank

sage: E.rank()
 

The elliptic curves in class 20160fg have rank \(1\).

Modular form 20160.2.a.fg

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.