# Properties

 Label 159936.bb Number of curves $6$ Conductor $159936$ CM no Rank $0$ Graph

# Learn more

Show commands: SageMath
sage: E = EllipticCurve("bb1")

sage: E.isogeny_class()

## Elliptic curves in class 159936.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
159936.bb1 159936in5 $$[0, -1, 0, -43021542209, 3434621350524225]$$ $$285531136548675601769470657/17941034271597192$$ $$553319069389720922779287552$$ $$[2]$$ $$283115520$$ $$4.5918$$
159936.bb2 159936in3 $$[0, -1, 0, -2693962049, 53452178201409]$$ $$70108386184777836280897/552468975892674624$$ $$17038684335583337339676524544$$ $$[2, 2]$$ $$141557760$$ $$4.2452$$
159936.bb3 159936in6 $$[0, -1, 0, -917606209, 122887441088833]$$ $$-2770540998624539614657/209924951154647363208$$ $$-6474291105862282807622498254848$$ $$[2]$$ $$283115520$$ $$4.5918$$
159936.bb4 159936in2 $$[0, -1, 0, -284510529, -464118461631]$$ $$82582985847542515777/44772582831427584$$ $$1380830307296116429295714304$$ $$[2, 2]$$ $$70778880$$ $$3.8987$$
159936.bb5 159936in1 $$[0, -1, 0, -220285249, -1256774022335]$$ $$38331145780597164097/55468445663232$$ $$1710701193155990406561792$$ $$[2]$$ $$35389440$$ $$3.5521$$ $$\Gamma_0(N)$$-optimal
159936.bb6 159936in4 $$[0, -1, 0, 1097336511, -3651486844095]$$ $$4738217997934888496063/2928751705237796928$$ $$-90325571172963862651147911168$$ $$[2]$$ $$141557760$$ $$4.2452$$

## Rank

sage: E.rank()

The elliptic curves in class 159936.bb have rank $$0$$.

## Complex multiplication

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

## Modular form 159936.2.a.bb

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 4 & 8 & 8 \\ 2 & 1 & 2 & 2 & 4 & 4 \\ 4 & 2 & 1 & 4 & 8 & 8 \\ 4 & 2 & 4 & 1 & 2 & 2 \\ 8 & 4 & 8 & 2 & 1 & 4 \\ 8 & 4 & 8 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.