Properties

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

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Show commands: SageMath
E = EllipticCurve("cb1")
 
E.isogeny_class()
 

Elliptic curves in class 20160cb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
20160.dy5 20160cb1 \([0, 0, 0, -552, -20536]\) \(-24918016/229635\) \(-171421608960\) \([2]\) \(16384\) \(0.83807\) \(\Gamma_0(N)\)-optimal
20160.dy4 20160cb2 \([0, 0, 0, -15132, -714544]\) \(32082281296/99225\) \(1185137049600\) \([2, 2]\) \(32768\) \(1.1846\)  
20160.dy1 20160cb3 \([0, 0, 0, -241932, -45802384]\) \(32779037733124/315\) \(15049359360\) \([2]\) \(65536\) \(1.5312\)  
20160.dy3 20160cb4 \([0, 0, 0, -21612, -43216]\) \(23366901604/13505625\) \(645241282560000\) \([2, 2]\) \(65536\) \(1.5312\)  
20160.dy2 20160cb5 \([0, 0, 0, -233292, 43224176]\) \(14695548366242/57421875\) \(5486745600000000\) \([4]\) \(131072\) \(1.8778\)  
20160.dy6 20160cb6 \([0, 0, 0, 86388, -345616]\) \(746185003198/432360075\) \(-41312648518041600\) \([2]\) \(131072\) \(1.8778\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 20160cb do not have complex multiplication.

Modular form 20160.2.a.cb

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

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.