Properties

Label 38976.bw
Number of curves $6$
Conductor $38976$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("38976.bw1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38976.bw

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38976.bw1 38976x4 [0, 1, 0, -13095937, 18236817503] [2] 786432  
38976.bw2 38976x6 [0, 1, 0, -2718017, -1402989537] [2] 1572864  
38976.bw3 38976x3 [0, 1, 0, -834177, 273251295] [2, 2] 786432  
38976.bw4 38976x2 [0, 1, 0, -818497, 284744735] [2, 2] 393216  
38976.bw5 38976x1 [0, 1, 0, -50177, 4615263] [2] 196608 \(\Gamma_0(N)\)-optimal
38976.bw6 38976x5 [0, 1, 0, 798783, 1214162847] [2] 1572864  

Rank

sage: E.rank()
 

The elliptic curves in class 38976.bw have rank \(1\).

Modular form 38976.2.a.bw

sage: E.q_eigenform(10)
 
\( q + q^{3} + 2q^{5} + q^{7} + q^{9} - 4q^{11} + 2q^{13} + 2q^{15} + 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.