Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("z1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5520.z

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.z1 5520y2 \([0, 1, 0, -1856, -30156]\) \(172715635009/7935000\) \(32501760000\) \([2]\) \(4608\) \(0.77868\)  
5520.z2 5520y1 \([0, 1, 0, 64, -1740]\) \(6967871/331200\) \(-1356595200\) \([2]\) \(2304\) \(0.43211\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5520.2.a.z

sage: E.q_eigenform(10)
 
\(q + q^{3} - q^{5} + 2q^{7} + q^{9} + 2q^{11} - 6q^{13} - q^{15} - 4q^{17} + O(q^{20})\)  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.