# Properties

 Label 116886a Number of curves $2$ Conductor $116886$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("a1")

sage: E.isogeny_class()

## Elliptic curves in class 116886a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.b2 116886a1 $$[1, 1, 0, 11009, -678575]$$ $$62570773/121716$$ $$-286999961157756$$ $$[2]$$ $$443520$$ $$1.4588$$ $$\Gamma_0(N)$$-optimal
116886.b1 116886a2 $$[1, 1, 0, -82161, -7293645]$$ $$26013270347/5398974$$ $$12730498277069034$$ $$[2]$$ $$887040$$ $$1.8053$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 116886.2.a.a

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} - 2q^{5} + q^{6} - q^{7} - q^{8} + q^{9} + 2q^{10} - q^{12} - 4q^{13} + q^{14} + 2q^{15} + q^{16} - 2q^{17} - q^{18} + 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.