Properties

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

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Show commands for: SageMath

sage: E = EllipticCurve("47040.cs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 47040fb

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
47040.cs3 47040fb1 [0, -1, 0, -7905, 258945] [2] 98304 \(\Gamma_0(N)\)-optimal
47040.cs2 47040fb2 [0, -1, 0, -23585, -1067583] [2, 2] 196608  
47040.cs4 47040fb3 [0, -1, 0, 54815, -6728063] [2] 393216  
47040.cs1 47040fb4 [0, -1, 0, -352865, -80555775] [2] 393216  

Rank

sage: E.rank()
 

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

Modular form 47040.2.a.cs

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 Cremona 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 Cremona labels.