Properties

Label 5040.f
Number of curves $4$
Conductor $5040$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5040.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5040.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5040.f1 5040u3 [0, 0, 0, -6723, 185922] [2] 6912  
5040.f2 5040u1 [0, 0, 0, -1683, -26542] [2] 2304 \(\Gamma_0(N)\)-optimal
5040.f3 5040u2 [0, 0, 0, -1203, -41998] [2] 4608  
5040.f4 5040u4 [0, 0, 0, 10557, 984258] [2] 13824  

Rank

sage: E.rank()
 

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

Modular form 5040.2.a.f

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

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.

\(\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.