Properties

Label 188760.cq
Number of curves $4$
Conductor $188760$
CM no
Rank $0$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("cq1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 188760.cq

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
188760.cq1 188760i4 \([0, 1, 0, -6645360, -6595864992]\) \(8945265872486162/804375\) \(2918398728960000\) \([2]\) \(4423680\) \(2.4056\)  
188760.cq2 188760i3 \([0, 1, 0, -730880, 73252320]\) \(11900808771122/6243874065\) \(22653754946489272320\) \([2]\) \(4423680\) \(2.4056\)  
188760.cq3 188760i2 \([0, 1, 0, -416280, -102672000]\) \(4397697224644/41409225\) \(75119583283430400\) \([2, 2]\) \(2211840\) \(2.0590\)  
188760.cq4 188760i1 \([0, 1, 0, -7300, -3862432]\) \(-94875856/14137695\) \(-6411722007525120\) \([4]\) \(1105920\) \(1.7125\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 188760.cq have rank \(0\).

Complex multiplication

The elliptic curves in class 188760.cq do not have complex multiplication.

Modular form 188760.2.a.cq

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

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.