Properties

Label 177870.cx
Number of curves $2$
Conductor $177870$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("177870.cx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 177870.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
177870.cx1 177870gl1 [1, 0, 1, -89059, -3917014] [2] 1881600 \(\Gamma_0(N)\)-optimal
177870.cx2 177870gl2 [1, 0, 1, 325971, -29980898] [2] 3763200  

Rank

sage: E.rank()
 

The elliptic curves in class 177870.cx have rank \(0\).

Modular form 177870.2.a.cx

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

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 LMFDB 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 LMFDB labels.