Properties

Label 57330.bu
Number of curves $6$
Conductor $57330$
CM no
Rank $2$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("57330.bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 57330.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
57330.bu1 57330cm6 [1, -1, 0, -3975624, -3050103330] [2] 1572864  
57330.bu2 57330cm4 [1, -1, 0, -372654, 87584328] [2] 786432  
57330.bu3 57330cm3 [1, -1, 0, -249174, -47329920] [2, 2] 786432  
57330.bu4 57330cm5 [1, -1, 0, -50724, -120796110] [2] 1572864  
57330.bu5 57330cm2 [1, -1, 0, -28674, 694980] [2, 2] 393216  
57330.bu6 57330cm1 [1, -1, 0, 6606, 81108] [2] 196608 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 57330.bu have rank \(2\).

Modular form 57330.2.a.bu

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 4q^{11} - q^{13} + q^{16} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.