Properties

Label 22050.cj
Number of curves $4$
Conductor $22050$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("cj1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.cj1 22050bq4 [1, -1, 0, -4118067, 3217561591] [2] 589824  
22050.cj2 22050bq2 [1, -1, 0, -259317, 49527841] [2, 2] 294912  
22050.cj3 22050bq1 [1, -1, 0, -38817, -1848659] [2] 147456 \(\Gamma_0(N)\)-optimal
22050.cj4 22050bq3 [1, -1, 0, 71433, 166944091] [2] 589824  

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 22050.cj do not have complex multiplication.

Modular form 22050.2.a.cj

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.