# Properties

 Label 116886.j Number of curves $2$ Conductor $116886$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 116886.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.j1 116886n2 $$[1, 0, 1, -1981983, -340077278]$$ $$486034459476995521/253095136942032$$ $$448373473896163151952$$ $$$$ $$6635520$$ $$2.6546$$
116886.j2 116886n1 $$[1, 0, 1, 467057, -41294398]$$ $$6360314548472639/4097346156288$$ $$-7258698653979725568$$ $$$$ $$3317760$$ $$2.3080$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 116886.j have rank $$1$$.

## Complex multiplication

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

## Modular form 116886.2.a.j

sage: E.q_eigenform(10)

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