Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("22050.dd1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050.dd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.dd1 22050es4 [1, -1, 1, -2951255, -1950620003] [2] 589824  
22050.dd2 22050es3 [1, -1, 1, -966755, 342138997] [2] 589824  
22050.dd3 22050es2 [1, -1, 1, -195005, -26757503] [2, 2] 294912  
22050.dd4 22050es1 [1, -1, 1, 25495, -2502503] [2] 147456 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 22050.2.a.dd

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.