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Properties

Label 164730.bx
Number of curves $2$
Conductor $164730$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bx1")
 
E.isogeny_class()
 

Elliptic curves in class 164730.bx

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
164730.bx1 164730bt2 \([1, 0, 1, -577573, -168639472]\) \(882774443450089/2166000000\) \(52281974454000000\) \([2]\) \(3311616\) \(2.0861\)  
164730.bx2 164730bt1 \([1, 0, 1, -22693, -4616944]\) \(-53540005609/350208000\) \(-8453169764352000\) \([2]\) \(1655808\) \(1.7395\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 164730.bx have rank \(0\).

Complex multiplication

The elliptic curves in class 164730.bx do not have complex multiplication.

Modular form 164730.2.a.bx

sage: E.q_eigenform(10)
 
\(q - q^{2} + q^{3} + q^{4} + q^{5} - q^{6} + 2 q^{7} - q^{8} + q^{9} - q^{10} - 4 q^{11} + q^{12} - 6 q^{13} - 2 q^{14} + q^{15} + q^{16} - q^{18} + q^{19} + O(q^{20})\) 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.

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.