Properties

Label 5520.k
Number of curves $2$
Conductor $5520$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("k1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5520.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.k1 5520d2 \([0, -1, 0, -518720, -143623200]\) \(7536914291382802562/17961229575\) \(36784598169600\) \([2]\) \(42240\) \(1.8444\)  
5520.k2 5520d1 \([0, -1, 0, -32040, -2291328]\) \(-3552342505518244/179863605135\) \(-184180331658240\) \([2]\) \(21120\) \(1.4978\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 5520.k have rank \(1\).

Complex multiplication

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

Modular form 5520.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{5} + q^{9} - 2 q^{11} - q^{15} + 6 q^{17} - 8 q^{19} + O(q^{20})\) Copy content 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.