Properties

Label 5520.l
Number of curves $2$
Conductor $5520$
CM no
Rank $0$
Graph

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

Elliptic curves in class 5520.l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.l1 5520t2 \([0, -1, 0, -62800, 6078400]\) \(6687281588245201/165600\) \(678297600\) \([2]\) \(11520\) \(1.2131\)  
5520.l2 5520t1 \([0, -1, 0, -3920, 96192]\) \(-1626794704081/8125440\) \(-33281802240\) \([2]\) \(5760\) \(0.86648\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

The elliptic curves in class 5520.l do not have complex multiplication.

Modular form 5520.2.a.l

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} + 2q^{11} + 4q^{13} - q^{15} + 6q^{17} + 8q^{19} + O(q^{20})\)  Toggle raw display

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.

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.