Properties

Label 166782.cj
Number of curves $4$
Conductor $166782$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("cj1")
 
E.isogeny_class()
 

Elliptic curves in class 166782.cj

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166782.cj1 166782e3 \([1, 0, 0, -81774, 8990058]\) \(1285429208617/614922\) \(28929547236282\) \([2]\) \(884736\) \(1.5379\)  
166782.cj2 166782e4 \([1, 0, 0, -45674, -3698370]\) \(223980311017/4278582\) \(201289659620742\) \([2]\) \(884736\) \(1.5379\)  
166782.cj3 166782e2 \([1, 0, 0, -5964, 89964]\) \(498677257/213444\) \(10041661024164\) \([2, 2]\) \(442368\) \(1.1913\)  
166782.cj4 166782e1 \([1, 0, 0, 1256, 10544]\) \(4657463/3696\) \(-173881576176\) \([2]\) \(221184\) \(0.84473\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 166782.cj have rank \(0\).

Complex multiplication

The elliptic curves in class 166782.cj do not have complex multiplication.

Modular form 166782.2.a.cj

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.