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Properties

Label 116886bv
Number of curves $2$
Conductor $116886$
CM no
Rank $0$
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Show commands: SageMath
E = EllipticCurve("bv1")
 
E.isogeny_class()
 

Elliptic curves in class 116886bv

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.bu2 116886bv1 \([1, 0, 0, -63, -154791]\) \(-15625/5842368\) \(-10350111296448\) \([2]\) \(268800\) \(1.1762\) \(\Gamma_0(N)\)-optimal
116886.bu1 116886bv2 \([1, 0, 0, -43623, -3456639]\) \(5182207647625/91449288\) \(162007992098568\) \([2]\) \(537600\) \(1.5228\)  

Rank

sage: E.rank()
 

The elliptic curves in class 116886bv have rank \(0\).

Complex multiplication

The elliptic curves in class 116886bv do not have complex multiplication.

Modular form 116886.2.a.bv

sage: E.q_eigenform(10)
 
\(q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} + q^{12} + 6 q^{13} + q^{14} + q^{16} - 2 q^{17} + q^{18} + 6 q^{19} + O(q^{20})\) 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 Cremona 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 Cremona labels.