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Properties

Label 187850.bo
Number of curves $2$
Conductor $187850$
CM no
Rank $0$
Graph

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

Elliptic curves in class 187850.bo

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
187850.bo1 187850m2 \([1, 1, 1, -81863013, -285122616469]\) \(-6434774386429585/140608\) \(-1325755977325000000\) \([]\) \(27216000\) \(3.0037\)  
187850.bo2 187850m1 \([1, 1, 1, -943013, -446056469]\) \(-9836106385/3407872\) \(-32131931852800000000\) \([]\) \(9072000\) \(2.4544\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 187850.bo have rank \(0\).

Complex multiplication

The elliptic curves in class 187850.bo do not have complex multiplication.

Modular form 187850.2.a.bo

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

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

Isogeny graph

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

The vertices are labelled with LMFDB labels.