Properties

Label 5520.x
Number of curves $4$
Conductor $5520$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("x1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5520.x

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.x1 5520ba4 \([0, 1, 0, -22118576, 40031686740]\) \(292169767125103365085489/72534787200\) \(297102488371200\) \([4]\) \(172032\) \(2.5928\)  
5520.x2 5520ba3 \([0, 1, 0, -1618096, 397291604]\) \(114387056741228939569/49503729150000000\) \(202767274598400000000\) \([2]\) \(172032\) \(2.5928\)  
5520.x3 5520ba2 \([0, 1, 0, -1382576, 624992340]\) \(71356102305927901489/35540674560000\) \(145574602997760000\) \([2, 2]\) \(86016\) \(2.2462\)  
5520.x4 5520ba1 \([0, 1, 0, -71856, 13148244]\) \(-10017490085065009/12502381363200\) \(-51209754063667200\) \([2]\) \(43008\) \(1.8996\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5520.2.a.x

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.