Properties

Label 86190i
Number of curves 4
Conductor 86190
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("86190.a1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 86190i

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86190.a4 86190i1 [1, 1, 0, 158012, 19086592] [2] 1419264 \(\Gamma_0(N)\)-optimal
86190.a3 86190i2 [1, 1, 0, -818808, 171275148] [2, 2] 2838528  
86190.a2 86190i3 [1, 1, 0, -5674178, -5081264118] [2] 5677056  
86190.a1 86190i4 [1, 1, 0, -11592558, 15183418398] [2] 5677056  

Rank

sage: E.rank()
 

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

Modular form 86190.2.a.a

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

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 Cremona 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 Cremona labels.