# Properties

 Label 73920.dw Number of curves $4$ Conductor $73920$ CM no Rank $2$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 73920.dw

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
73920.dw1 73920bu4 $$[0, -1, 0, -198385, 17998225]$$ $$52702650535889104/22020583921875$$ $$360785246976000000$$ $$[2]$$ $$995328$$ $$2.0660$$
73920.dw2 73920bu2 $$[0, -1, 0, -171025, 27280177]$$ $$33766427105425744/9823275$$ $$160944537600$$ $$[2]$$ $$331776$$ $$1.5167$$
73920.dw3 73920bu1 $$[0, -1, 0, -10645, 432565]$$ $$-130287139815424/2250652635$$ $$-2304668298240$$ $$[2]$$ $$165888$$ $$1.1701$$ $$\Gamma_0(N)$$-optimal
73920.dw4 73920bu3 $$[0, -1, 0, 41195, 2042197]$$ $$7549996227362816/6152409907875$$ $$-6300067745664000$$ $$[2]$$ $$497664$$ $$1.7194$$

## Rank

sage: E.rank()

The elliptic curves in class 73920.dw have rank $$2$$.

## Complex multiplication

The elliptic curves in class 73920.dw do not have complex multiplication.

## Modular form 73920.2.a.dw

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{7} + q^{9} + q^{11} - 2q^{13} - q^{15} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 3 & 6 & 2 \\ 3 & 1 & 2 & 6 \\ 6 & 2 & 1 & 3 \\ 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.