Properties

Label 22050eo
Number of curves 8
Conductor 22050
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("22050.fe1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 22050eo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
22050.fe7 22050eo1 [1, -1, 1, 2315020, 1021026647] [2] 1179648 \(\Gamma_0(N)\)-optimal
22050.fe6 22050eo2 [1, -1, 1, -11796980, 9149538647] [2, 2] 2359296  
22050.fe5 22050eo3 [1, -1, 1, -83238980, -285763037353] [2, 2] 4718592  
22050.fe4 22050eo4 [1, -1, 1, -166146980, 824117538647] [2] 4718592  
22050.fe8 22050eo5 [1, -1, 1, 14001520, -913547705353] [2] 9437184  
22050.fe2 22050eo6 [1, -1, 1, -1323551480, -18533240537353] [2, 2] 9437184  
22050.fe3 22050eo7 [1, -1, 1, -1315282730, -18776242562353] [2] 18874368  
22050.fe1 22050eo8 [1, -1, 1, -21176820230, -1186143682262353] [2] 18874368  

Rank

sage: E.rank()
 

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

Modular form 22050.2.a.fe

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

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 Cremona numbering.

\(\left(\begin{array}{rrrrrrrr} 1 & 2 & 4 & 4 & 8 & 8 & 16 & 16 \\ 2 & 1 & 2 & 2 & 4 & 4 & 8 & 8 \\ 4 & 2 & 1 & 4 & 2 & 2 & 4 & 4 \\ 4 & 2 & 4 & 1 & 8 & 8 & 16 & 16 \\ 8 & 4 & 2 & 8 & 1 & 4 & 8 & 8 \\ 8 & 4 & 2 & 8 & 4 & 1 & 2 & 2 \\ 16 & 8 & 4 & 16 & 8 & 2 & 1 & 4 \\ 16 & 8 & 4 & 16 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.