# Properties

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

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 116886o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
116886.t2 116886o1 $$[1, 0, 1, -198146, 33903956]$$ $$7110352307247726625/6866458324992$$ $$830841457324032$$ $$[]$$ $$829440$$ $$1.7839$$ $$\Gamma_0(N)$$-optimal
116886.t1 116886o2 $$[1, 0, 1, -16046066, 24738734612]$$ $$3776104682692733708238625/3408048$$ $$412373808$$ $$[]$$ $$2488320$$ $$2.3332$$

## Rank

sage: E.rank()

The elliptic curves in class 116886o have rank $$2$$.

## Complex multiplication

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

## Modular form 116886.2.a.o

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 Cremona 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 Cremona labels.