Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("190575.el1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 190575ds

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
190575.el4 190575ds1 [1, -1, 0, -926217, 343218816] [2] 2457600 \(\Gamma_0(N)\)-optimal
190575.el3 190575ds2 [1, -1, 0, -1062342, 235816191] [2, 2] 4915200  
190575.el6 190575ds3 [1, -1, 0, 3429783, 1704741066] [2] 9830400  
190575.el2 190575ds4 [1, -1, 0, -7732467, -8108510184] [2, 2] 9830400  
190575.el5 190575ds5 [1, -1, 0, 843408, -25114470309] [2] 19660800  
190575.el1 190575ds6 [1, -1, 0, -123030342, -525219479559] [2] 19660800  

Rank

sage: E.rank()
 

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

Modular form 190575.2.a.el

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{4} + q^{7} - 3q^{8} + 6q^{13} + q^{14} - q^{16} - 2q^{17} - 4q^{19} + O(q^{20}) \)

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.