# Properties

 Label 1584.n Number of curves 4 Conductor 1584 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1584.n1")

sage: E.isogeny_class()

## Elliptic curves in class 1584.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1584.n1 1584c4 [0, 0, 0, -6339, 194258] [4] 1536
1584.n2 1584c3 [0, 0, 0, -939, -6838] [2] 1536
1584.n3 1584c2 [0, 0, 0, -399, 2990] [2, 2] 768
1584.n4 1584c1 [0, 0, 0, 6, 155] [2] 384 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form1584.2.a.n

sage: E.q_eigenform(10)

$$q + 2q^{5} - 4q^{7} - q^{11} + 6q^{13} - 6q^{17} + 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.