Properties

Label 22050bi
Number of curves 6
Conductor 22050
CM no
Rank 1
Graph

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Show commands for: SageMath

sage: E = EllipticCurve("22050.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.ba5 22050bi1 [1, -1, 0, -5742, 340416] [2] 55296 \(\Gamma_0(N)\)-optimal
22050.ba4 22050bi2 [1, -1, 0, -115992, 15224166] [2] 110592  
22050.ba6 22050bi3 [1, -1, 0, 49383, -7101459] [2] 165888  
22050.ba3 22050bi4 [1, -1, 0, -391617, -77220459] [2] 331776  
22050.ba2 22050bi5 [1, -1, 0, -1879992, -994555584] [2] 497664  
22050.ba1 22050bi6 [1, -1, 0, -30103992, -63567163584] [2] 995328  

Rank

sage: E.rank()
 

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

Modular form 22050.2.a.ba

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

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 6 & 9 & 18 \\ 2 & 1 & 6 & 3 & 18 & 9 \\ 3 & 6 & 1 & 2 & 3 & 6 \\ 6 & 3 & 2 & 1 & 6 & 3 \\ 9 & 18 & 3 & 6 & 1 & 2 \\ 18 & 9 & 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.