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Properties

Label 218010.ch
Number of curves $4$
Conductor $218010$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("ch1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 218010.ch

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
218010.ch1 218010b3 [1, 0, 0, -141710, 20381022] [2] 1769472  
218010.ch2 218010b2 [1, 0, 0, -14960, -177828] [2, 2] 884736  
218010.ch3 218010b1 [1, 0, 0, -11580, -480000] [2] 442368 \(\Gamma_0(N)\)-optimal
218010.ch4 218010b4 [1, 0, 0, 57710, -1384150] [2] 1769472  

Rank

sage: E.rank()
 

The elliptic curves in class 218010.ch have rank \(0\).

Complex multiplication

The elliptic curves in class 218010.ch do not have complex multiplication.

Modular form 218010.2.a.ch

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.