Properties

Label 159936.bg
Number of curves $2$
Conductor $159936$
CM no
Rank $1$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
sage: E = EllipticCurve("bg1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 159936.bg

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159936.bg1 159936io2 \([0, -1, 0, -4094523169, -100843240667231]\) \(717647917494305598319/844621814448\) \(8934794661425712709238784\) \([2]\) \(86704128\) \(4.0704\)  
159936.bg2 159936io1 \([0, -1, 0, -253801249, -1602826976351]\) \(-170915990723796079/6015674034432\) \(-63636542803299112379744256\) \([2]\) \(43352064\) \(3.7238\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 159936.bg have rank \(1\).

Complex multiplication

The elliptic curves in class 159936.bg do not have complex multiplication.

Modular form 159936.2.a.bg

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