Properties

Label 86190.b
Number of curves 4
Conductor 86190
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("86190.b1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 86190.b

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86190.b1 86190c4 [1, 1, 0, -12948783, 17898665517] [2] 7741440  
86190.b2 86190c3 [1, 1, 0, -10853183, -13695181443] [2] 7741440  
86190.b3 86190c2 [1, 1, 0, -1084983, 72119637] [2, 2] 3870720  
86190.b4 86190c1 [1, 1, 0, 267017, 9116437] [2] 1935360 \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 86190.b have rank \(1\).

Modular form 86190.2.a.b

sage: E.q_eigenform(10)
 
\( q - q^{2} - q^{3} + q^{4} - q^{5} + q^{6} - 4q^{7} - q^{8} + q^{9} + q^{10} + 4q^{11} - q^{12} + 4q^{14} + q^{15} + q^{16} - q^{17} - q^{18} - 8q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.