# Properties

 Label 5166.o Number of curves $2$ Conductor $5166$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 5166.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
5166.o1 5166r2 [1, -1, 0, -86501814, 309682215836] [] 345744
5166.o2 5166r1 [1, -1, 0, -174174, -25711084] [] 49392 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 5166.o have rank $$0$$.

## Complex multiplication

The elliptic curves in class 5166.o do not have complex multiplication.

## Modular form5166.2.a.o

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + q^{7} - q^{8} - q^{10} + 2q^{11} - q^{14} + q^{16} + 3q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 7 \\ 7 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.