# Properties

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

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 $$[0, -1, 0, -4094523169, -100843240667231]$$ $$717647917494305598319/844621814448$$ $$8934794661425712709238784$$ $$$$ $$86704128$$ $$4.0704$$
159936.bg2 159936io1 $$[0, -1, 0, -253801249, -1602826976351]$$ $$-170915990723796079/6015674034432$$ $$-63636542803299112379744256$$ $$$$ $$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)

$$q - q^{3} - 2q^{5} + q^{9} - 2q^{11} + 4q^{13} + 2q^{15} + q^{17} - 2q^{19} + O(q^{20})$$ ## 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. 