Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("22050.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.e1 22050s2 [1, -1, 0, -7947, 274511] [2] 36864  
22050.e2 22050s1 [1, -1, 0, -597, 2561] [2] 18432 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Modular form 22050.2.a.e

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.