Properties

Label 22050z
Number of curves $2$
Conductor $22050$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("22050.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.i1 22050z1 [1, -1, 0, -358542, -185734634] [] 580608 \(\Gamma_0(N)\)-optimal
22050.i2 22050z2 [1, -1, 0, 3114333, 4110211741] [] 1741824  

Rank

sage: E.rank()
 

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

Modular form 22050.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} - q^{8} - 3q^{11} - 5q^{13} + q^{16} + 5q^{19} + O(q^{20}) \)

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 Cremona numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.