Properties

Label 146523.n
Number of curves $2$
Conductor $146523$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("n1")
 
E.isogeny_class()
 

Elliptic curves in class 146523.n

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
146523.n1 146523l2 \([1, 0, 0, -21681, -6833646]\) \(-276301129/4782969\) \(-19510922280339009\) \([]\) \(739200\) \(1.8070\)  
146523.n2 146523l1 \([1, 0, 0, -2896, 60449]\) \(-658489/9\) \(-36713242449\) \([]\) \(105600\) \(0.83402\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 146523.n have rank \(0\).

Complex multiplication

The elliptic curves in class 146523.n do not have complex multiplication.

Modular form 146523.2.a.n

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

\(\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.