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Properties

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

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Show commands: SageMath
E = EllipticCurve("cz1")
 
E.isogeny_class()
 

Elliptic curves in class 177870.cz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
177870.cz1 177870gn1 \([1, 0, 1, -29615479, -62033233594]\) \(13782741913468081/701662500\) \(146242168269197962500\) \([2]\) \(16588800\) \(2.9393\) \(\Gamma_0(N)\)-optimal
177870.cz2 177870gn2 \([1, 0, 1, -28014649, -69036544678]\) \(-11666347147400401/3126621093750\) \(-651657809995847402343750\) \([2]\) \(33177600\) \(3.2859\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 177870.2.a.cz

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} - q^{5} - q^{6} - q^{8} + q^{9} + q^{10} + q^{12} + 4 q^{13} - q^{15} + q^{16} - 4 q^{17} - q^{18} + 8 q^{19} + O(q^{20})\) 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.