# Properties

 Label 1584r Number of curves 2 Conductor 1584 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1584.e1")

sage: E.isogeny_class()

## Elliptic curves in class 1584r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1584.e2 1584r1 [0, 0, 0, 24, -25]  192 $$\Gamma_0(N)$$-optimal
1584.e1 1584r2 [0, 0, 0, -111, -214]  384

## Rank

sage: E.rank()

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

## Modular form1584.2.a.e

sage: E.q_eigenform(10)

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

## 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 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. 