Properties

Label 86490.bu
Number of curves $2$
Conductor $86490$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
E = EllipticCurve("bu1")
 
E.isogeny_class()
 

Elliptic curves in class 86490.bu

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
86490.bu1 86490cf2 \([1, -1, 1, -17406293, -9789531843]\) \(901456690969801/457629750000\) \(296081955904220007750000\) \([2]\) \(14745600\) \(3.1962\)  
86490.bu2 86490cf1 \([1, -1, 1, 4043227, -1183984419]\) \(11298232190519/7472736000\) \(-4834786835505946464000\) \([2]\) \(7372800\) \(2.8496\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 86490.bu have rank \(0\).

Complex multiplication

The elliptic curves in class 86490.bu do not have complex multiplication.

Modular form 86490.2.a.bu

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