Properties

Label 5040.l
Number of curves $6$
Conductor $5040$
CM no
Rank $1$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5040.l1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5040.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5040.l1 5040m5 [0, 0, 0, -94323, -11149742] [2] 16384  
5040.l2 5040m3 [0, 0, 0, -6123, -160022] [2, 2] 8192  
5040.l3 5040m2 [0, 0, 0, -1623, 22678] [2, 2] 4096  
5040.l4 5040m1 [0, 0, 0, -1578, 24127] [2] 2048 \(\Gamma_0(N)\)-optimal
5040.l5 5040m4 [0, 0, 0, 2157, 112642] [2] 8192  
5040.l6 5040m6 [0, 0, 0, 10077, -863102] [2] 16384  

Rank

sage: E.rank()
 

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

Modular form 5040.2.a.l

sage: E.q_eigenform(10)
 
\( q - q^{5} + q^{7} - 4q^{11} - 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20}) \)

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.

\(\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.