# Properties

 Label 159936.bh Number of curves $4$ Conductor $159936$ CM no Rank $2$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("bh1")

sage: E.isogeny_class()

## Elliptic curves in class 159936.bh

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159936.bh1 159936ip4 $$[0, -1, 0, -15927809, -24461764095]$$ $$14489843500598257/6246072$$ $$192634978232696832$$ $$[2]$$ $$7077888$$ $$2.6592$$
159936.bh2 159936ip3 $$[0, -1, 0, -2129409, 632909313]$$ $$34623662831857/14438442312$$ $$445295702721033142272$$ $$[2]$$ $$7077888$$ $$2.6592$$
159936.bh3 159936ip2 $$[0, -1, 0, -1000449, -377961471]$$ $$3590714269297/73410624$$ $$2264055546636140544$$ $$[2, 2]$$ $$3538944$$ $$2.3127$$
159936.bh4 159936ip1 $$[0, -1, 0, 3071, -17697791]$$ $$103823/4386816$$ $$-135293702133252096$$ $$[2]$$ $$1769472$$ $$1.9661$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 159936.bh have rank $$2$$.

## Complex multiplication

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

## Modular form 159936.2.a.bh

sage: E.q_eigenform(10)

$$q - q^{3} - 2q^{5} + q^{9} - 6q^{13} + 2q^{15} - q^{17} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.