# Properties

 Label 1584q Number of curves 4 Conductor 1584 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1584.o1")

sage: E.isogeny_class()

## Elliptic curves in class 1584q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1584.o3 1584q1 [0, 0, 0, -939, -10982]  768 $$\Gamma_0(N)$$-optimal
1584.o2 1584q2 [0, 0, 0, -1659, 8170] [2, 2] 1536
1584.o1 1584q3 [0, 0, 0, -21099, 1178458]  3072
1584.o4 1584q4 [0, 0, 0, 6261, 63610]  3072

## Rank

sage: E.rank()

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

## Modular form1584.2.a.o

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 