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Properties

Label 2550.k
Number of curves $2$
Conductor $2550$
CM no
Rank $0$
Graph

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

Elliptic curves in class 2550.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2550.k1 2550o2 \([1, 0, 1, -1455988826, -21382165598452]\) \(873851835888094527083289145/83719665273003835392\) \(32702994247267123200000000\) \([]\) \(1285200\) \(3.9323\)  
2550.k2 2550o1 \([1, 0, 1, -38539451, 48878897798]\) \(16206164115169540524745/6736014906011025408\) \(2631255822660556800000000\) \([3]\) \(428400\) \(3.3830\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 2550.k have rank \(0\).

Complex multiplication

The elliptic curves in class 2550.k do not have complex multiplication.

Modular form 2550.2.a.k

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