Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("5040.z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5040y

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5040.z3 5040y1 [0, 0, 0, -747, -6886] [2] 2304 \(\Gamma_0(N)\)-optimal
5040.z4 5040y2 [0, 0, 0, 1173, -36454] [2] 4608  
5040.z1 5040y3 [0, 0, 0, -15147, 716634] [2] 6912  
5040.z2 5040y4 [0, 0, 0, -10827, 1133946] [2] 13824  

Rank

sage: E.rank()
 

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

Modular form 5040.2.a.z

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.