Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("22050.c1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050.c

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.c1 22050k4 [1, -1, 0, -266667, 13921991] [2] 414720  
22050.c2 22050k2 [1, -1, 0, -156417, -23771259] [2] 138240  
22050.c3 22050k1 [1, -1, 0, -9417, -398259] [2] 69120 \(\Gamma_0(N)\)-optimal
22050.c4 22050k3 [1, -1, 0, 64083, 1684241] [2] 207360  

Rank

sage: E.rank()
 

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

Modular form 22050.2.a.c

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

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.