Properties

Label 22050cn
Number of curves $4$
Conductor $22050$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("22050.y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050cn

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.y4 22050cn1 [1, -1, 0, -1332, -25124] [2] 23040 \(\Gamma_0(N)\)-optimal
22050.y2 22050cn2 [1, -1, 0, -23382, -1370174] [2] 46080  
22050.y3 22050cn3 [1, -1, 0, -12357, 2543701] [2] 115200  
22050.y1 22050cn4 [1, -1, 0, -365157, 84746101] [2] 230400  

Rank

sage: E.rank()
 

The elliptic curves in class 22050cn have rank \(0\).

Modular form 22050.2.a.y

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{8} - 2q^{11} + 6q^{13} + q^{16} - 2q^{17} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 5 & 10 \\ 2 & 1 & 10 & 5 \\ 5 & 10 & 1 & 2 \\ 10 & 5 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.