Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("47040.gg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47040.gg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47040.gg1 47040df4 [0, 1, 0, -352865, 80555775] [2] 393216  
47040.gg2 47040df2 [0, 1, 0, -23585, 1067583] [2, 2] 196608  
47040.gg3 47040df1 [0, 1, 0, -7905, -258945] [2] 98304 \(\Gamma_0(N)\)-optimal
47040.gg4 47040df3 [0, 1, 0, 54815, 6728063] [2] 393216  

Rank

sage: E.rank()
 

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

Modular form 47040.2.a.gg

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} + q^{9} - 6q^{13} + q^{15} - 2q^{17} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.