Properties

Label 41616.be
Number of curves 4
Conductor 41616
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("41616.be1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 41616.be

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
41616.be1 41616ca4 [0, 0, 0, -4703475, -2713145294] [2] 1990656  
41616.be2 41616ca3 [0, 0, 0, -4287315, -3416372462] [2] 995328  
41616.be3 41616ca2 [0, 0, 0, -1790355, 921845842] [2] 663552  
41616.be4 41616ca1 [0, 0, 0, -125715, 10621906] [2] 331776 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 41616.be have rank \(1\).

Modular form 41616.2.a.be

sage: E.q_eigenform(10)
 
\( q - 4q^{7} - 6q^{11} + 2q^{13} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.