Properties

Label 41280.bu
Number of curves $4$
Conductor $41280$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bu1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 41280.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
41280.bu1 41280u4 \([0, -1, 0, -53665, 4770337]\) \(65202655558249/512820150\) \(134432725401600\) \([4]\) \(147456\) \(1.5392\)  
41280.bu2 41280u2 \([0, -1, 0, -5665, -39263]\) \(76711450249/41602500\) \(10905845760000\) \([2, 2]\) \(73728\) \(1.1926\)  
41280.bu3 41280u1 \([0, -1, 0, -4385, -110175]\) \(35578826569/51600\) \(13526630400\) \([2]\) \(36864\) \(0.84606\) \(\Gamma_0(N)\)-optimal
41280.bu4 41280u3 \([0, -1, 0, 21855, -330975]\) \(4403686064471/2721093750\) \(-713318400000000\) \([2]\) \(147456\) \(1.5392\)  

Rank

sage: E.rank()
 

The elliptic curves in class 41280.bu have rank \(1\).

Complex multiplication

The elliptic curves in class 41280.bu do not have complex multiplication.

Modular form 41280.2.a.bu

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

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.