Properties

Label 166410.bo
Number of curves $2$
Conductor $166410$
CM no
Rank $1$
Graph

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

Elliptic curves in class 166410.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166410.bo1 166410i2 \([1, -1, 1, -9540884723, 358702145436647]\) \(262147686417280027/22500\) \(8243775317294067307500\) \([2]\) \(116244480\) \(4.0915\)  
166410.bo2 166410i1 \([1, -1, 1, -596347223, 5604005271647]\) \(64014401080027/18750000\) \(6869812764411722756250000\) \([2]\) \(58122240\) \(3.7450\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 166410.bo have rank \(1\).

Complex multiplication

The elliptic curves in class 166410.bo do not have complex multiplication.

Modular form 166410.2.a.bo

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{4} - q^{5} - 4 q^{7} + q^{8} - q^{10} + 2 q^{11} - 2 q^{13} - 4 q^{14} + q^{16} + 2 q^{17} - 4 q^{19} + O(q^{20})\) 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.