Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("dz1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47040.dz

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47040.dz1 47040gk4 [0, 1, 0, -1171361, 487569375] [2] 589824  
47040.dz2 47040gk2 [0, 1, 0, -73761, 7479135] [2, 2] 294912  
47040.dz3 47040gk1 [0, 1, 0, -11041, -285601] [2] 147456 \(\Gamma_0(N)\)-optimal
47040.dz4 47040gk3 [0, 1, 0, 20319, 25335519] [2] 589824  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 47040.2.a.dz

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.