Properties

Label 54080.bs
Number of curves 4
Conductor 54080
CM no
Rank 1
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("54080.bs1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54080.bs

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54080.bs1 54080cw4 [0, 0, 0, -72332, 7487376] [2] 147456  
54080.bs2 54080cw2 [0, 0, 0, -4732, 105456] [2, 2] 73728  
54080.bs3 54080cw1 [0, 0, 0, -1352, -17576] [2] 36864 \(\Gamma_0(N)\)-optimal
54080.bs4 54080cw3 [0, 0, 0, 8788, 597584] [2] 147456  

Rank

sage: E.rank()
 

The elliptic curves in class 54080.bs have rank \(1\).

Modular form 54080.2.a.bs

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

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.