Properties

Label 86190x
Number of curves 2
Conductor 86190
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("86190.v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 86190x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86190.v1 86190x1 [1, 0, 1, -111109054, 450778669616] [2] 8171520 \(\Gamma_0(N)\)-optimal
86190.v2 86190x2 [1, 0, 1, -110987374, 451815285872] [2] 16343040  

Rank

sage: E.rank()
 

The elliptic curves in class 86190x have rank \(0\).

Modular form 86190.2.a.v

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

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.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.