Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("do1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 190575do

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
190575.dx6 190575do1 [1, -1, 0, 952308, -103907201909] [2] 22118400 \(\Gamma_0(N)\)-optimal
190575.dx5 190575do2 [1, -1, 0, -325883817, -2224093144784] [2, 2] 44236800  
190575.dx4 190575do3 [1, -1, 0, -692740692, 3701012243341] [2] 88473600  
190575.dx2 190575do4 [1, -1, 0, -5188404942, -143845020910409] [2, 2] 88473600  
190575.dx3 190575do5 [1, -1, 0, -5162677317, -145342188592034] [2] 176947200  
190575.dx1 190575do6 [1, -1, 0, -83014470567, -9206145580482284] [2] 176947200  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 190575.2.a.do

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

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.