# Properties

 Label 1134.h Number of curves $2$ Conductor $1134$ CM no Rank $0$ Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("1134.h1")

sage: E.isogeny_class()

## Elliptic curves in class 1134.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1134.h1 1134h1 [1, -1, 1, -11, 19] [3] 144 $$\Gamma_0(N)$$-optimal
1134.h2 1134h2 [1, -1, 1, 79, -161] [] 432

## Rank

sage: E.rank()

The elliptic curves in class 1134.h have rank $$0$$.

## Modular form1134.2.a.h

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + 3q^{5} + q^{7} + q^{8} + 3q^{10} + 6q^{11} + 2q^{13} + q^{14} + q^{16} - 6q^{17} - 7q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.