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Properties

Label 16170.bo
Number of curves $2$
Conductor $16170$
CM no
Rank $0$
Graph

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Show commands: SageMath
E = EllipticCurve("bo1")
 
E.isogeny_class()
 

Elliptic curves in class 16170.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
16170.bo1 16170bp2 \([1, 1, 1, -132105, 22411227]\) \(-902612375329/249562500\) \(-70495229328562500\) \([]\) \(254016\) \(1.9486\)  
16170.bo2 16170bp1 \([1, 1, 1, 11955, -235005]\) \(668944031/475200\) \(-134232238324800\) \([]\) \(84672\) \(1.3993\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 16170.bo have rank \(0\).

Complex multiplication

The elliptic curves in class 16170.bo do not have complex multiplication.

Modular form 16170.2.a.bo

sage: E.q_eigenform(10)
 
\(q + q^{2} - q^{3} + q^{4} + q^{5} - q^{6} + q^{8} + q^{9} + q^{10} - q^{11} - q^{12} + 4 q^{13} - q^{15} + q^{16} - 3 q^{17} + q^{18} + 7 q^{19} + O(q^{20})\) 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.