Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("86640.di1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 86640eh

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
86640.di4 86640eh1 [0, 1, 0, -57880, 9126548] [2] 829440 \(\Gamma_0(N)\)-optimal
86640.di3 86640eh2 [0, 1, 0, -1097560, 442049300] [2, 2] 1658880  
86640.di2 86640eh3 [0, 1, 0, -1270840, 292959188] [2] 3317760  
86640.di1 86640eh4 [0, 1, 0, -17559160, 28314830420] [2] 3317760  

Rank

sage: E.rank()
 

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

Modular form 86640.2.a.di

sage: E.q_eigenform(10)
 
\( q + q^{3} + q^{5} - 4q^{7} + q^{9} + 4q^{11} + 2q^{13} + q^{15} - 2q^{17} + O(q^{20}) \)

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 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.