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Properties

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

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

Elliptic curves in class 177870.cx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177870.cx1 177870gl1 \([1, 0, 1, -89059, -3917014]\) \(1092727/540\) \(38603993240084580\) \([2]\) \(1881600\) \(1.8758\) \(\Gamma_0(N)\)-optimal
177870.cx2 177870gl2 \([1, 0, 1, 325971, -29980898]\) \(53582633/36450\) \(-2605769543705709150\) \([2]\) \(3763200\) \(2.2223\)  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 177870.cx do not have complex multiplication.

Modular form 177870.2.a.cx

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