Properties

Label 22218.y
Number of curves $6$
Conductor $22218$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("22218.y1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22218.y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22218.y1 22218t6 [1, 1, 1, -41861897, 104231607419] [2] 2162688  
22218.y2 22218t4 [1, 1, 1, -9370717, -11044581181] [2] 1081344  
22218.y3 22218t3 [1, 1, 1, -2684157, 1538915331] [2, 2] 1081344  
22218.y4 22218t2 [1, 1, 1, -610477, -157354909] [2, 2] 540672  
22218.y5 22218t1 [1, 1, 1, 66643, -13534621] [4] 270336 \(\Gamma_0(N)\)-optimal
22218.y6 22218t5 [1, 1, 1, 3314703, 7448992203] [2] 2162688  

Rank

sage: E.rank()
 

The elliptic curves in class 22218.y have rank \(1\).

Modular form 22218.2.a.y

sage: E.q_eigenform(10)
 
\( q + q^{2} - q^{3} + q^{4} + 2q^{5} - q^{6} - q^{7} + q^{8} + q^{9} + 2q^{10} + 4q^{11} - q^{12} - 2q^{13} - q^{14} - 2q^{15} + q^{16} + 6q^{17} + q^{18} - 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.