Properties

Label 166410.ct
Number of curves $2$
Conductor $166410$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("ct1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 166410.ct

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166410.ct1 166410f2 \([1, -1, 1, -29621327, 72605965079]\) \(-337335507529/72000000\) \(-613490256170721288000000\) \([3]\) \(24966144\) \(3.2858\)  
166410.ct2 166410f1 \([1, -1, 1, 2579008, -578956309]\) \(222641831/145800\) \(-1242317768745710608200\) \([]\) \(8322048\) \(2.7364\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 166410.ct have rank \(0\).

Complex multiplication

The elliptic curves in class 166410.ct do not have complex multiplication.

Modular form 166410.2.a.ct

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} + q^{5} + 2q^{7} + q^{8} + q^{10} + 3q^{11} - 4q^{13} + 2q^{14} + q^{16} + 3q^{17} - q^{19} + O(q^{20})\)  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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.