# Properties

 Label 1584.r Number of curves $2$ Conductor $1584$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 1584.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1584.r1 1584i2 $$[0, 0, 0, -2403, 45090]$$ $$19034163/121$$ $$9755209728$$ $$[2]$$ $$1536$$ $$0.75376$$
1584.r2 1584i1 $$[0, 0, 0, -243, -270]$$ $$19683/11$$ $$886837248$$ $$[2]$$ $$768$$ $$0.40719$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1584.r have rank $$0$$.

## Complex multiplication

The elliptic curves in class 1584.r do not have complex multiplication.

## Modular form1584.2.a.r

sage: E.q_eigenform(10)

$$q + 4q^{5} + 2q^{7} - q^{11} - 2q^{13} - 2q^{17} + 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.