Properties

Label 5550g
Number of curves $2$
Conductor $5550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("g1")
 
E.isogeny_class()
 

Elliptic curves in class 5550g

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.j2 5550g1 \([1, 1, 0, -54185, 4961925]\) \(-140754878313089741/4409857671168\) \(-551232208896000\) \([2]\) \(40320\) \(1.6051\) \(\Gamma_0(N)\)-optimal
5550.j1 5550g2 \([1, 1, 0, -873385, 313800325]\) \(589429221475670903501/552712568832\) \(69089071104000\) \([2]\) \(80640\) \(1.9517\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5550g have rank \(0\).

Complex multiplication

The elliptic curves in class 5550g do not have complex multiplication.

Modular form 5550.2.a.g

sage: E.q_eigenform(10)
 
\(q - q^{2} - q^{3} + q^{4} + q^{6} + 2 q^{7} - q^{8} + q^{9} - 2 q^{11} - q^{12} + 6 q^{13} - 2 q^{14} + q^{16} - 6 q^{17} - q^{18} - 4 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.