Properties

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

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Show commands for: SageMath
sage: E = EllipticCurve("f1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 5520.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5520.f1 5520m3 \([0, -1, 0, -170296, -26932880]\) \(133345896593725369/340006815000\) \(1392667914240000\) \([2]\) \(46080\) \(1.7823\)  
5520.f2 5520m2 \([0, -1, 0, -14776, -59024]\) \(87109155423289/49979073600\) \(204714285465600\) \([2, 2]\) \(23040\) \(1.4357\)  
5520.f3 5520m1 \([0, -1, 0, -9656, 366960]\) \(24310870577209/114462720\) \(468839301120\) \([2]\) \(11520\) \(1.0891\) \(\Gamma_0(N)\)-optimal
5520.f4 5520m4 \([0, -1, 0, 58824, -530064]\) \(5495662324535111/3207841648920\) \(-13139319393976320\) \([2]\) \(46080\) \(1.7823\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5520.2.a.f

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.