Properties

Label 16650bu
Number of curves $6$
Conductor $16650$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("16650.cb1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 16650bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16650.cb5 16650bu1 [1, -1, 1, -190130, -109799503] [2] 331776 \(\Gamma_0(N)\)-optimal
16650.cb4 16650bu2 [1, -1, 1, -4798130, -4035815503] [2, 2] 663552  
16650.cb1 16650bu3 [1, -1, 1, -76726130, -258660935503] [2] 1327104  
16650.cb3 16650bu4 [1, -1, 1, -6598130, -731015503] [2, 2] 1327104  
16650.cb2 16650bu5 [1, -1, 1, -68203130, 215872164497] [2] 2654208  
16650.cb6 16650bu6 [1, -1, 1, 26206870, -5848595503] [2] 2654208  

Rank

sage: E.rank()
 

The elliptic curves in class 16650bu have rank \(1\).

Modular form 16650.2.a.cb

sage: E.q_eigenform(10)
 
\( q + q^{2} + q^{4} + q^{8} - 4q^{11} + 2q^{13} + q^{16} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.