Properties

Label 182070.cg
Number of curves $4$
Conductor $182070$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("182070.cg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 182070.cg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
182070.cg1 182070ch3 [1, -1, 1, -273593, -54944459] [2] 1492992  
182070.cg2 182070ch4 [1, -1, 1, -195563, -86999183] [2] 2985984  
182070.cg3 182070ch1 [1, -1, 1, -13493, 531981] [2] 497664 \(\Gamma_0(N)\)-optimal
182070.cg4 182070ch2 [1, -1, 1, 21187, 2793117] [2] 995328  

Rank

sage: E.rank()
 

The elliptic curves in class 182070.cg have rank \(0\).

Modular form 182070.2.a.cg

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

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.

\(\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.