Properties

Label 204624.bu
Number of curves $6$
Conductor $204624$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("204624.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 204624.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
204624.bu1 204624y4 [0, 0, 0, -1443827091, -21116449256686] [2] 37748736  
204624.bu2 204624y5 [0, 0, 0, -299661411, 1623086947874] [2] 75497472  
204624.bu3 204624y3 [0, 0, 0, -91968051, -316644418510] [2, 2] 37748736  
204624.bu4 204624y2 [0, 0, 0, -90239331, -329943461470] [2, 2] 18874368  
204624.bu5 204624y1 [0, 0, 0, -5532051, -5362105966] [2] 9437184 \(\Gamma_0(N)\)-optimal
204624.bu6 204624y6 [0, 0, 0, 88065789, -1405237035454] [2] 75497472  

Rank

sage: E.rank()
 

The elliptic curves in class 204624.bu have rank \(0\).

Modular form 204624.2.a.bu

sage: E.q_eigenform(10)
 
\( q - 2q^{5} + 4q^{11} + 2q^{13} + 2q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.