Properties

Label 159936.gv
Number of curves $6$
Conductor $159936$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("159936.gv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 159936.gv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
159936.gv1 159936s6 [0, 1, 0, -43021542209, -3434621350524225] [2] 283115520  
159936.gv2 159936s4 [0, 1, 0, -2693962049, -53452178201409] [2, 2] 141557760  
159936.gv3 159936s5 [0, 1, 0, -917606209, -122887441088833] [2] 283115520  
159936.gv4 159936s2 [0, 1, 0, -284510529, 464118461631] [2, 2] 70778880  
159936.gv5 159936s1 [0, 1, 0, -220285249, 1256774022335] [2] 35389440 \(\Gamma_0(N)\)-optimal
159936.gv6 159936s3 [0, 1, 0, 1097336511, 3651486844095] [2] 141557760  

Rank

sage: E.rank()
 

The elliptic curves in class 159936.gv have rank \(0\).

Modular form 159936.2.a.gv

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.