# Properties

 Label 1089.h Number of curves $2$ Conductor $1089$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 1089.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1089.h1 1089c2 $$[1, -1, 0, -2019, -34226]$$ $$19034163/121$$ $$5787689787$$ $$$$ $$960$$ $$0.71026$$
1089.h2 1089c1 $$[1, -1, 0, -204, 259]$$ $$19683/11$$ $$526153617$$ $$$$ $$480$$ $$0.36368$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1089.h have rank $$0$$.

## Complex multiplication

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

## Modular form1089.2.a.h

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 