Properties

Label 28050y
Number of curves 6
Conductor 28050
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("28050.bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 28050y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28050.bg4 28050y1 [1, 0, 1, -182751, 30054898] [2] 147456 \(\Gamma_0(N)\)-optimal
28050.bg3 28050y2 [1, 0, 1, -184751, 29362898] [2, 2] 294912  
28050.bg5 28050y3 [1, 0, 1, 95749, 110707898] [2] 589824  
28050.bg2 28050y4 [1, 0, 1, -497251, -96262102] [2, 2] 589824  
28050.bg6 28050y5 [1, 0, 1, 1308999, -634524602] [2] 1179648  
28050.bg1 28050y6 [1, 0, 1, -7303501, -7596749602] [2] 1179648  

Rank

sage: E.rank()
 

The elliptic curves in class 28050y have rank \(0\).

Modular form 28050.2.a.bg

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} - q^{11} + q^{12} - 6q^{13} + q^{16} - q^{17} - q^{18} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.