# Properties

 Label 169338b Number of curves 2 Conductor 169338 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("169338.w1")
sage: E.isogeny_class()

## Elliptic curves in class 169338b

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
169338.w2 169338b1 [1, 0, 0, -764, -33840] 2 338688 $$\Gamma_0(N)$$-optimal
169338.w1 169338b2 [1, 0, 0, -21044, -1173576] 2 677376

## Rank

sage: E.rank()

The elliptic curves in class 169338b have rank $$1$$.

## Modular form None

sage: E.q_eigenform(10)
$$q + q^{2} + q^{3} + q^{4} - 2q^{5} + q^{6} + 4q^{7} + q^{8} + q^{9} - 2q^{10} + 4q^{11} + q^{12} + 4q^{14} - 2q^{15} + q^{16} - 4q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.