# Properties

 Label 166410u Number of curves $2$ Conductor $166410$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 166410u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
166410.cl2 166410u1 [1, -1, 1, -170670443, -889883315269] [2] 74511360 $$\Gamma_0(N)$$-optimal
166410.cl1 166410u2 [1, -1, 1, -2758678763, -55769117342533] [2] 149022720

## Rank

sage: E.rank()

The elliptic curves in class 166410u have rank $$0$$.

## Complex multiplication

The elliptic curves in class 166410u do not have complex multiplication.

## Modular form 166410.2.a.u

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} - q^{5} + 4q^{7} + q^{8} - q^{10} + 4q^{11} + 4q^{13} + 4q^{14} + q^{16} - 4q^{17} - 4q^{19} + O(q^{20})$$

## 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.