Properties

Label 190575.dx
Number of curves $6$
Conductor $190575$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("dx1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 190575.dx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
190575.dx1 190575do6 \([1, -1, 0, -83014470567, -9206145580482284]\) \(3135316978843283198764801/571725\) \(11536945696508203125\) \([2]\) \(176947200\) \(4.4521\)  
190575.dx2 190575do4 \([1, -1, 0, -5188404942, -143845020910409]\) \(765458482133960722801/326869475625\) \(6595960278336152431640625\) \([2, 2]\) \(88473600\) \(4.1055\)  
190575.dx3 190575do5 \([1, -1, 0, -5162677317, -145342188592034]\) \(-754127868744065783521/15825714261328125\) \(-319350047735183888067626953125\) \([2]\) \(176947200\) \(4.4521\)  
190575.dx4 190575do3 \([1, -1, 0, -692740692, 3701012243341]\) \(1821931919215868881/761147600816295\) \(15359339783366300714919609375\) \([2]\) \(88473600\) \(4.1055\)  
190575.dx5 190575do2 \([1, -1, 0, -325883817, -2224093144784]\) \(189674274234120481/3859869269025\) \(77889023835519240003515625\) \([2, 2]\) \(44236800\) \(3.7590\)  
190575.dx6 190575do1 \([1, -1, 0, 952308, -103907201909]\) \(4733169839/231139696095\) \(-4664211154235732516484375\) \([2]\) \(22118400\) \(3.4124\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 190575.dx have rank \(0\).

Complex multiplication

The elliptic curves in class 190575.dx do not have complex multiplication.

Modular form 190575.2.a.dx

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

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 4 & 8 \\ 2 & 1 & 2 & 4 & 2 & 4 \\ 4 & 2 & 1 & 8 & 4 & 8 \\ 8 & 4 & 8 & 1 & 2 & 4 \\ 4 & 2 & 4 & 2 & 1 & 2 \\ 8 & 4 & 8 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.