# Properties

 Label 1089h Number of curves $2$ Conductor $1089$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1089h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1089.c2 1089h1 [1, -1, 1, -23, 168] [] 144 $$\Gamma_0(N)$$-optimal
1089.c1 1089h2 [1, -1, 1, -32693, -2267130] [] 1584

## Rank

sage: E.rank()

The elliptic curves in class 1089h have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1089h do not have complex multiplication.

## Modular form1089.2.a.h

sage: E.q_eigenform(10)

$$q - q^{2} - q^{4} - q^{5} - 2q^{7} + 3q^{8} + q^{10} + q^{13} + 2q^{14} - q^{16} + 5q^{17} + 6q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 11 \\ 11 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 