Properties

Label 39600.dv
Number of curves 4
Conductor 39600
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("39600.dv1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 39600.dv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
39600.dv1 39600df3 [0, 0, 0, -289875, -59840750] [2] 331776  
39600.dv2 39600df4 [0, 0, 0, -145875, -119312750] [2] 663552  
39600.dv3 39600df1 [0, 0, 0, -19875, 1017250] [2] 110592 \(\Gamma_0(N)\)-optimal
39600.dv4 39600df2 [0, 0, 0, 16125, 4293250] [2] 221184  

Rank

sage: E.rank()
 

The elliptic curves in class 39600.dv have rank \(1\).

Modular form 39600.2.a.dv

sage: E.q_eigenform(10)
 
\( q + 2q^{7} - q^{11} + 4q^{13} - 6q^{17} + 4q^{19} + O(q^{20}) \)

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 LMFDB numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.