Properties

Label 5520.v
Number of curves $4$
Conductor $5520$
CM no
Rank $1$
Graph

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Show commands: SageMath
sage: E = EllipticCurve("v1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5520.v

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.v1 5520g3 \([0, 1, 0, -1056, -13356]\) \(63649751618/1164375\) \(2384640000\) \([2]\) \(3072\) \(0.59423\)  
5520.v2 5520g2 \([0, 1, 0, -136, 260]\) \(273671716/119025\) \(121881600\) \([2, 2]\) \(1536\) \(0.24766\)  
5520.v3 5520g1 \([0, 1, 0, -116, 444]\) \(680136784/345\) \(88320\) \([2]\) \(768\) \(-0.098917\) \(\Gamma_0(N)\)-optimal
5520.v4 5520g4 \([0, 1, 0, 464, 2420]\) \(5382838942/4197615\) \(-8596715520\) \([2]\) \(3072\) \(0.59423\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5520.2.a.v

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.