# Properties

 Label 1584.h Number of curves 4 Conductor 1584 CM no Rank 1 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1584.h1")

sage: E.isogeny_class()

## Elliptic curves in class 1584.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1584.h1 1584l3 [0, 0, 0, -11595, -478726] [2] 2304
1584.h2 1584l4 [0, 0, 0, -5835, -954502] [2] 4608
1584.h3 1584l1 [0, 0, 0, -795, 8138] [2] 768 $$\Gamma_0(N)$$-optimal
1584.h4 1584l2 [0, 0, 0, 645, 34346] [2] 1536

## Rank

sage: E.rank()

The elliptic curves in class 1584.h have rank $$1$$.

## Modular form1584.2.a.h

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.