Properties

Label 176610dq
Number of curves $2$
Conductor $176610$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("dq1")
 
E.isogeny_class()
 

Elliptic curves in class 176610dq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
176610.a1 176610dq1 \([1, 1, 0, -5904678, -5503982508]\) \(1569388636061/6914880\) \(100315173565617030720\) \([2]\) \(9354240\) \(2.6904\) \(\Gamma_0(N)\)-optimal
176610.a2 176610dq2 \([1, 1, 0, -2977998, -10958728692]\) \(-201333092381/3458880600\) \(-50178485777301352241400\) \([2]\) \(18708480\) \(3.0370\)  

Rank

sage: E.rank()
 

The elliptic curves in class 176610dq have rank \(0\).

Complex multiplication

The elliptic curves in class 176610dq do not have complex multiplication.

Modular form 176610.2.a.dq

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + q^{10} - 6 q^{11} - q^{12} - 4 q^{13} + q^{14} + q^{15} + q^{16} - 2 q^{17} - q^{18} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.