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Properties

Label 55470.k
Number of curves $2$
Conductor $55470$
CM no
Rank $0$
Graph

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

Elliptic curves in class 55470.k

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
55470.k1 55470n2 \([1, 0, 1, -2470303, -1494607744]\) \(263732349218689/4160250\) \(26298450624602250\) \([2]\) \(1064448\) \(2.2846\)  
55470.k2 55470n1 \([1, 0, 1, -159053, -21879244]\) \(70393838689/8062500\) \(50965989582562500\) \([2]\) \(532224\) \(1.9380\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 55470.k have rank \(0\).

Complex multiplication

The elliptic curves in class 55470.k do not have complex multiplication.

Modular form 55470.2.a.k

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} - 2 q^{7} - q^{8} + q^{9} - q^{10} + 2 q^{11} + q^{12} - 2 q^{13} + 2 q^{14} + q^{15} + q^{16} + 4 q^{17} - q^{18} + 2 q^{19} + O(q^{20})\) 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 LMFDB 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 LMFDB labels.