Properties

Label 38720.bm
Number of curves 4
Conductor 38720
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("38720.bm1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 38720.bm

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
38720.bm1 38720bu4 [0, 0, 0, -51788, -4536048] [2] 81920  
38720.bm2 38720bu2 [0, 0, 0, -3388, -63888] [2, 2] 40960  
38720.bm3 38720bu1 [0, 0, 0, -968, 10648] [2] 20480 \(\Gamma_0(N)\)-optimal
38720.bm4 38720bu3 [0, 0, 0, 6292, -362032] [2] 81920  

Rank

sage: E.rank()
 

The elliptic curves in class 38720.bm have rank \(1\).

Modular form 38720.2.a.bm

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

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.