Properties

Label 5520u
Number of curves $6$
Conductor $5520$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("5520.i1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5520u

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5520.i5 5520u1 [0, -1, 0, -6720, -230400] [2] 9216 \(\Gamma_0(N)\)-optimal
5520.i4 5520u2 [0, -1, 0, -110400, -14082048] [2, 2] 18432  
5520.i1 5520u3 [0, -1, 0, -1766400, -903022848] [2] 36864  
5520.i3 5520u4 [0, -1, 0, -113280, -13305600] [2, 4] 36864  
5520.i2 5520u5 [0, -1, 0, -413280, 87734400] [4] 73728  
5520.i6 5520u6 [0, -1, 0, 140640, -64699008] [4] 73728  

Rank

sage: E.rank()
 

The elliptic curves in class 5520u have rank \(0\).

Modular form 5520.2.a.i

sage: E.q_eigenform(10)
 
\( q - q^{3} + q^{5} + q^{9} - 4q^{11} - 2q^{13} - q^{15} - 6q^{17} - 4q^{19} + O(q^{20}) \)

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 Cremona numbering.

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

Isogeny graph

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

The vertices are labelled with Cremona labels.