Properties

Label 47040.bk
Number of curves $4$
Conductor $47040$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bk1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47040.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47040.bk1 47040m4 [0, -1, 0, -1171361, -487569375] [2] 589824  
47040.bk2 47040m2 [0, -1, 0, -73761, -7479135] [2, 2] 294912  
47040.bk3 47040m1 [0, -1, 0, -11041, 285601] [2] 147456 \(\Gamma_0(N)\)-optimal
47040.bk4 47040m3 [0, -1, 0, 20319, -25335519] [2] 589824  

Rank

sage: E.rank()
 

The elliptic curves in class 47040.bk have rank \(0\).

Complex multiplication

The elliptic curves in class 47040.bk do not have complex multiplication.

Modular form 47040.2.a.bk

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} + 4q^{11} - 2q^{13} + q^{15} + 6q^{17} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.