Properties

Label 86190.l
Number of curves $4$
Conductor $86190$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("86190.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 86190.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86190.l1 86190g4 [1, 1, 0, -63765393, -196012766763] [2] 12386304  
86190.l2 86190g2 [1, 1, 0, -4006993, -3028989803] [2, 2] 6193152  
86190.l3 86190g1 [1, 1, 0, -545873, 85325973] [2] 3096576 \(\Gamma_0(N)\)-optimal
86190.l4 86190g3 [1, 1, 0, 373487, -9292200107] [2] 12386304  

Rank

sage: E.rank()
 

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

Modular form 86190.2.a.l

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.