Properties

Label 54096.bi
Number of curves $6$
Conductor $54096$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("54096.bi1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 54096.bi

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
54096.bi1 54096bw6 [0, -1, 0, -62041072, -188068013888] [2] 4718592  
54096.bi2 54096bw4 [0, -1, 0, -13887792, 19924489152] [2] 2359296  
54096.bi3 54096bw3 [0, -1, 0, -3978032, -2777240640] [2, 2] 2359296  
54096.bi4 54096bw2 [0, -1, 0, -904752, 283746240] [2, 2] 1179648  
54096.bi5 54096bw1 [0, -1, 0, 98768, 24436672] [2] 589824 \(\Gamma_0(N)\)-optimal
54096.bi6 54096bw5 [0, -1, 0, 4912528, -13438800192] [4] 4718592  

Rank

sage: E.rank()
 

The elliptic curves in class 54096.bi have rank \(0\).

Modular form 54096.2.a.bi

sage: E.q_eigenform(10)
 
\( q - q^{3} + 2q^{5} + q^{9} + 4q^{11} + 2q^{13} - 2q^{15} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.