Properties

Label 156702.bk
Number of curves $2$
Conductor $156702$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bk1")
 
E.isogeny_class()
 

Elliptic curves in class 156702.bk

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
156702.bk1 156702x2 \([1, 1, 1, -53078957, 148822004435]\) \(-58547782891689619297/43006704\) \(-12148329421069296\) \([]\) \(11104128\) \(2.8307\)  
156702.bk2 156702x1 \([1, 1, 1, -641117, 213165875]\) \(-103170428183137/9961795584\) \(-2813960688077500416\) \([]\) \(3701376\) \(2.2814\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 156702.bk have rank \(0\).

Complex multiplication

The elliptic curves in class 156702.bk do not have complex multiplication.

Modular form 156702.2.a.bk

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} - 3 q^{5} - q^{6} + q^{8} + q^{9} - 3 q^{10} - q^{12} - q^{13} + 3 q^{15} + q^{16} + 3 q^{17} + q^{18} + q^{19} + O(q^{20})\) 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.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

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

The vertices are labelled with LMFDB labels.