Properties

Label 140790.be
Number of curves $6$
Conductor $140790$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("140790.be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 140790.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
140790.be1 140790bx5 [1, 0, 1, -3254423, 2259471368] [2] 3538944  
140790.be2 140790bx4 [1, 0, 1, -305053, -64824244] [2] 1769472  
140790.be3 140790bx3 [1, 0, 1, -203973, 35083228] [2, 2] 1769472  
140790.be4 140790bx6 [1, 0, 1, -41523, 89471488] [2] 3538944  
140790.be5 140790bx2 [1, 0, 1, -23473, -511372] [2, 2] 884736  
140790.be6 140790bx1 [1, 0, 1, 5407, -60844] [2] 442368 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 140790.be have rank \(0\).

Modular form 140790.2.a.be

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - q^{8} + q^{9} - q^{10} + 4q^{11} + q^{12} - q^{13} + q^{15} + q^{16} - 6q^{17} - q^{18} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 4 & 8 \\ 8 & 1 & 4 & 8 & 2 & 4 \\ 2 & 4 & 1 & 2 & 2 & 4 \\ 4 & 8 & 2 & 1 & 4 & 8 \\ 4 & 2 & 2 & 4 & 1 & 2 \\ 8 & 4 & 4 & 8 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.