Properties

Label 161700.bf
Number of curves $2$
Conductor $161700$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bf1")
 
E.isogeny_class()
 

Elliptic curves in class 161700.bf

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
161700.bf1 161700da1 \([0, -1, 0, -6747708, -6744386088]\) \(-2888047810000/35937\) \(-422795211300000000\) \([]\) \(4898880\) \(2.5293\) \(\Gamma_0(N)\)-optimal
161700.bf2 161700da2 \([0, -1, 0, -3072708, -14032646088]\) \(-272709010000/7073843073\) \(-83223056369537700000000\) \([]\) \(14696640\) \(3.0786\)  

Rank

sage: E.rank()
 

The elliptic curves in class 161700.bf have rank \(0\).

Complex multiplication

The elliptic curves in class 161700.bf do not have complex multiplication.

Modular form 161700.2.a.bf

sage: E.q_eigenform(10)
 
\(q - q^{3} + q^{9} - q^{11} + 4 q^{13} - 3 q^{17} - 5 q^{19} + O(q^{20})\) 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.