Properties

Label 5040bo
Number of curves $4$
Conductor $5040$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("bo1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5040bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5040.bg3 5040bo1 [0, 0, 0, -507, -2774] [2] 3072 \(\Gamma_0(N)\)-optimal
5040.bg2 5040bo2 [0, 0, 0, -3387, 73834] [2, 2] 6144  
5040.bg1 5040bo3 [0, 0, 0, -53787, 4801354] [2] 12288  
5040.bg4 5040bo4 [0, 0, 0, 933, 249226] [4] 12288  

Rank

sage: E.rank()
 

The elliptic curves in class 5040bo have rank \(1\).

Complex multiplication

The elliptic curves in class 5040bo do not have complex multiplication.

Modular form 5040.2.a.bo

sage: E.q_eigenform(10)
 
\( q + q^{5} + q^{7} - 4q^{11} - 2q^{13} + 6q^{17} + O(q^{20}) \)

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 Cremona 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 Cremona labels.