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Properties

Label 5550a
Number of curves $2$
Conductor $5550$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("a1")
 
E.isogeny_class()
 

Elliptic curves in class 5550a

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.h2 5550a1 \([1, 1, 0, 50, -500]\) \(857375/7992\) \(-124875000\) \([]\) \(1728\) \(0.23479\) \(\Gamma_0(N)\)-optimal
5550.h1 5550a2 \([1, 1, 0, -3700, -88250]\) \(-358667682625/303918\) \(-4748718750\) \([]\) \(5184\) \(0.78409\)  

Rank

sage: E.rank()
 

The elliptic curves in class 5550a have rank \(1\).

Complex multiplication

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

Modular form 5550.2.a.a

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

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.