Properties

Label 22050.w
Number of curves $2$
Conductor $22050$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("22050.w1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050.w

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.w1 22050bl2 [1, -1, 0, -48240117, -128949609209] [] 1152000  
22050.w2 22050bl1 [1, -1, 0, 9693, -25468619] [] 230400 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 22050.w have rank \(1\).

Modular form 22050.2.a.w

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

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 LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.