Properties

Label 86640.j
Number of curves $4$
Conductor $86640$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("86640.j1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 86640.j

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86640.j1 86640bw4 [0, -1, 0, -3587016, -2609861520] [2] 2211840  
86640.j2 86640bw2 [0, -1, 0, -294696, -12879504] [2, 2] 1105920  
86640.j3 86640bw1 [0, -1, 0, -179176, 29077360] [2] 552960 \(\Gamma_0(N)\)-optimal
86640.j4 86640bw3 [0, -1, 0, 1149304, -102985104] [2] 2211840  

Rank

sage: E.rank()
 

The elliptic curves in class 86640.j have rank \(1\).

Modular form 86640.2.a.j

sage: E.q_eigenform(10)
 
\( q - q^{3} - q^{5} + q^{9} - 4q^{11} - 2q^{13} + q^{15} + 2q^{17} + O(q^{20}) \)

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.