# Properties

 Label 116886.bt Number of curves $2$ Conductor $116886$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bt1")

sage: E.isogeny_class()

## Elliptic curves in class 116886.bt

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.bt1 116886bu2 $$[1, 0, 0, -1941573928, -32929197342832]$$ $$3776104682692733708238625/3408048$$ $$730545355674288$$ $$[]$$ $$27371520$$ $$3.5321$$
116886.bt2 116886bu1 $$[1, 0, 0, -23975608, -45150141376]$$ $$7110352307247726625/6866458324992$$ $$1471886322978419453952$$ $$$$ $$9123840$$ $$2.9828$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 116886.bt have rank $$0$$.

## Complex multiplication

The elliptic curves in class 116886.bt do not have complex multiplication.

## Modular form 116886.2.a.bt

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{7} + q^{8} + q^{9} + q^{12} + 2q^{13} + q^{14} + q^{16} + 6q^{17} + q^{18} + 2q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 