Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("22050.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050cw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.f2 22050cw1 [1, -1, 0, -399492, -96378584] [] 345600 \(\Gamma_0(N)\)-optimal
22050.f1 22050cw2 [1, -1, 0, -32293242, -70626217334] [] 1036800  

Rank

sage: E.rank()
 

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

Modular form 22050.2.a.f

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{8} - 6q^{11} + 4q^{13} + q^{16} - 3q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.