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Properties

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

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Show commands: SageMath
E = EllipticCurve("l1")
 
E.isogeny_class()
 

Elliptic curves in class 5550l

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
5550.c2 5550l1 \([1, 1, 0, -315, 2025]\) \(27790593389/11988\) \(1498500\) \([2]\) \(1280\) \(0.14497\) \(\Gamma_0(N)\)-optimal
5550.c1 5550l2 \([1, 1, 0, -365, 1275]\) \(43206601229/17964018\) \(2245502250\) \([2]\) \(2560\) \(0.49154\)  

Rank

sage: E.rank()
 

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

Complex multiplication

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

Modular form 5550.2.a.l

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