Properties

Label 22050.q
Number of curves $2$
Conductor $22050$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("22050.q1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050.q

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.q1 22050y2 [1, -1, 0, -160092, 24820816] [] 155520  
22050.q2 22050y1 [1, -1, 0, 5283, 179941] [] 51840 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 22050.2.a.q

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{8} - 3q^{11} + 4q^{13} + q^{16} - 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.