# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 116886.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.u1 116886j2 $$[1, 0, 1, -3688772954056, 2726910926533633046]$$ $$-3133382230165522315000208250857964625/153574604080128$$ $$-272066779178795639808$$ $$[]$$ $$1077753600$$ $$5.3134$$
116886.u2 116886j1 $$[1, 0, 1, -45540006856, 3740684175189014]$$ $$-5895856113332931416918127084625/215771481613620039647232$$ $$-382252341738906331057489969152$$ $$[]$$ $$359251200$$ $$4.7641$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 116886.2.a.u

sage: E.q_eigenform(10)

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