# Properties

 Label 1155.h Number of curves $2$ Conductor $1155$ CM no Rank $1$ Graph # Related objects

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

E.isogeny_class()

## Elliptic curves in class 1155.h

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.h1 1155j2 $$[0, 1, 1, -841, -9674]$$ $$-65860951343104/3493875$$ $$-3493875$$ $$[]$$ $$432$$ $$0.32335$$
1155.h2 1155j1 $$[0, 1, 1, -1, -35]$$ $$-262144/509355$$ $$-509355$$ $$$$ $$144$$ $$-0.22596$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 1155.h have rank $$1$$.

## Complex multiplication

The elliptic curves in class 1155.h do not have complex multiplication.

## Modular form1155.2.a.h

sage: E.q_eigenform(10)

$$q + q^{3} - 2 q^{4} - q^{5} + q^{7} + q^{9} - q^{11} - 2 q^{12} - 4 q^{13} - q^{15} + 4 q^{16} + 3 q^{17} - q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 