Properties

Label 39984df
Number of curves 6
Conductor 39984
CM no
Rank 0
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("39984.dn1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 39984df

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
39984.dn5 39984df1 [0, 1, 0, -26672, 1546068] [2] 147456 \(\Gamma_0(N)\)-optimal
39984.dn4 39984df2 [0, 1, 0, -89392, -8514220] [2, 2] 294912  
39984.dn6 39984df3 [0, 1, 0, 177168, -49351212] [2] 589824  
39984.dn2 39984df4 [0, 1, 0, -1359472, -610532140] [2, 2] 589824  
39984.dn3 39984df5 [0, 1, 0, -1288912, -676660972] [2] 1179648  
39984.dn1 39984df6 [0, 1, 0, -21751312, -39053228908] [2] 1179648  

Rank

sage: E.rank()
 

The elliptic curves in class 39984df have rank \(0\).

Modular form 39984.2.a.dn

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} + q^{9} + 4q^{11} + 2q^{13} + 2q^{15} - q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.