Properties

Label 5040.ba
Number of curves $8$
Conductor $5040$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5040.ba1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5040.ba

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5040.ba1 5040bj7 [0, 0, 0, -928947, 216809714] [2] 110592  
5040.ba2 5040bj4 [0, 0, 0, -829587, 290831186] [2] 36864  
5040.ba3 5040bj6 [0, 0, 0, -388947, -90882286] [2, 2] 55296  
5040.ba4 5040bj3 [0, 0, 0, -386067, -92329774] [2] 27648  
5040.ba5 5040bj2 [0, 0, 0, -51987, 4518866] [2, 2] 18432  
5040.ba6 5040bj5 [0, 0, 0, -11667, 11349074] [2] 36864  
5040.ba7 5040bj1 [0, 0, 0, -5907, -61486] [2] 9216 \(\Gamma_0(N)\)-optimal
5040.ba8 5040bj8 [0, 0, 0, 104973, -305935054] [2] 110592  

Rank

sage: E.rank()
 

The elliptic curves in class 5040.ba have rank \(0\).

Modular form 5040.2.a.ba

sage: E.q_eigenform(10)
 
\( q + q^{5} - q^{7} + 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrrrr} 1 & 3 & 2 & 4 & 6 & 12 & 12 & 4 \\ 3 & 1 & 6 & 12 & 2 & 4 & 4 & 12 \\ 2 & 6 & 1 & 2 & 3 & 6 & 6 & 2 \\ 4 & 12 & 2 & 1 & 6 & 12 & 3 & 4 \\ 6 & 2 & 3 & 6 & 1 & 2 & 2 & 6 \\ 12 & 4 & 6 & 12 & 2 & 1 & 4 & 3 \\ 12 & 4 & 6 & 3 & 2 & 4 & 1 & 12 \\ 4 & 12 & 2 & 4 & 6 & 3 & 12 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.