Properties

Label 139656.e
Number of curves 4
Conductor 139656
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("139656.e1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 139656.e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
139656.e1 139656ba4 [0, -1, 0, -249864, -47983572] [2] 788480  
139656.e2 139656ba2 [0, -1, 0, -17104, -593636] [2, 2] 394240  
139656.e3 139656ba1 [0, -1, 0, -6524, 197748] [2] 197120 \(\Gamma_0(N)\)-optimal
139656.e4 139656ba3 [0, -1, 0, 46376, -4021556] [2] 788480  

Rank

sage: E.rank()
 

The elliptic curves in class 139656.e have rank \(0\).

Modular form 139656.2.a.e

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

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.