Properties

Label 2520e
Number of curves $6$
Conductor $2520$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("2520.f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 2520e

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2520.f4 2520e1 [0, 0, 0, -1578, -24127] [2] 1024 \(\Gamma_0(N)\)-optimal
2520.f3 2520e2 [0, 0, 0, -1623, -22678] [2, 2] 2048  
2520.f2 2520e3 [0, 0, 0, -6123, 160022] [2, 2] 4096  
2520.f5 2520e4 [0, 0, 0, 2157, -112642] [2] 4096  
2520.f1 2520e5 [0, 0, 0, -94323, 11149742] [2] 8192  
2520.f6 2520e6 [0, 0, 0, 10077, 863102] [2] 8192  

Rank

sage: E.rank()
 

The elliptic curves in class 2520e have rank \(0\).

Modular form 2520.2.a.f

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.