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Properties

Label 550k
Number of curves $3$
Conductor $550$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("k1")
 
E.isogeny_class()
 

Elliptic curves in class 550k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
550.j2 550k1 \([1, 1, 1, -28, -69]\) \(-19465109/22\) \(-2750\) \([]\) \(48\) \(-0.42631\) \(\Gamma_0(N)\)-optimal
550.j3 550k2 \([1, 1, 1, 197, 681]\) \(6761990971/5153632\) \(-644204000\) \([5]\) \(240\) \(0.37841\)  
550.j1 550k3 \([1, 1, 1, -30328, 2020281]\) \(-24680042791780949/369098752\) \(-46137344000\) \([5]\) \(1200\) \(1.1831\)  

Rank

sage: E.rank()
 

The elliptic curves in class 550k have rank \(0\).

Complex multiplication

The elliptic curves in class 550k do not have complex multiplication.

Modular form 550.2.a.k

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - q^{6} + 3 q^{7} + q^{8} - 2 q^{9} + q^{11} - q^{12} + 4 q^{13} + 3 q^{14} + q^{16} + 3 q^{17} - 2 q^{18} - 5 q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with Cremona labels.