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Properties

Label 52290cr
Number of curves $2$
Conductor $52290$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("cr1")
 
E.isogeny_class()
 

Elliptic curves in class 52290cr

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
52290.ck2 52290cr1 \([1, -1, 1, -5252, 116579]\) \(21973174804729/4842576900\) \(3530238560100\) \([2]\) \(122880\) \(1.1212\) \(\Gamma_0(N)\)-optimal
52290.ck1 52290cr2 \([1, -1, 1, -27302, -1629781]\) \(3087199234101529/199326394890\) \(145308941874810\) \([2]\) \(245760\) \(1.4677\)  

Rank

sage: E.rank()
 

The elliptic curves in class 52290cr have rank \(0\).

Complex multiplication

The elliptic curves in class 52290cr do not have complex multiplication.

Modular form 52290.2.a.cr

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