Properties

Label 161700bt
Number of curves $4$
Conductor $161700$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands for: SageMath
sage: E = EllipticCurve("bt1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 161700bt

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.dg3 161700bt1 \([0, 1, 0, -3260133, -2300347512]\) \(-130287139815424/2250652635\) \(-66196757963778750000\) \([2]\) \(5971968\) \(2.6012\) \(\Gamma_0(N)\)-optimal
161700.dg2 161700bt2 \([0, 1, 0, -52376508, -145916628012]\) \(33766427105425744/9823275\) \(4622793921900000000\) \([2]\) \(11943936\) \(2.9478\)  
161700.dg4 161700bt3 \([0, 1, 0, 12615867, -11014287012]\) \(7549996227362816/6152409907875\) \(-180956218312896468750000\) \([2]\) \(17915904\) \(3.1505\)  
161700.dg1 161700bt4 \([0, 1, 0, -60755508, -96125082012]\) \(52702650535889104/22020583921875\) \(10362798711298687500000000\) \([2]\) \(35831808\) \(3.4971\)  

Rank

sage: E.rank()
 

The elliptic curves in class 161700bt have rank \(0\).

Complex multiplication

The elliptic curves in class 161700bt do not have complex multiplication.

Modular form 161700.2.a.bt

sage: E.q_eigenform(10)
 
\(q + q^{3} + q^{9} - q^{11} + 2q^{13} - 6q^{17} - 8q^{19} + O(q^{20})\)  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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.