# Properties

 Label 33600.dw Number of curves $2$ Conductor $33600$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("dw1")

sage: E.isogeny_class()

## Elliptic curves in class 33600.dw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
33600.dw1 33600co2 $$[0, 1, 0, -560833, -171229537]$$ $$-7620530425/526848$$ $$-1348730880000000000$$ $$[]$$ $$622080$$ $$2.2298$$
33600.dw2 33600co1 $$[0, 1, 0, 39167, -229537]$$ $$2595575/1512$$ $$-3870720000000000$$ $$[]$$ $$207360$$ $$1.6805$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 33600.dw have rank $$0$$.

## Complex multiplication

The elliptic curves in class 33600.dw do not have complex multiplication.

## Modular form 33600.2.a.dw

sage: E.q_eigenform(10)

$$q + q^{3} - q^{7} + q^{9} - 6q^{11} - q^{13} - 3q^{17} + 4q^{19} + O(q^{20})$$

## 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 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.