# Properties

 Label 1155.l Number of curves $4$ Conductor $1155$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("l1")

E.isogeny_class()

## Elliptic curves in class 1155.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.l1 1155h3 $$[1, 0, 1, -2054, -35989]$$ $$957681397954009/31185$$ $$31185$$ $$$$ $$384$$ $$0.36359$$
1155.l2 1155h4 $$[1, 0, 1, -204, 151]$$ $$932288503609/527295615$$ $$527295615$$ $$$$ $$384$$ $$0.36359$$
1155.l3 1155h2 $$[1, 0, 1, -129, -569]$$ $$234770924809/1334025$$ $$1334025$$ $$[2, 2]$$ $$192$$ $$0.017018$$
1155.l4 1155h1 $$[1, 0, 1, -4, -19]$$ $$-4826809/144375$$ $$-144375$$ $$$$ $$96$$ $$-0.32956$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1155.2.a.l

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} - q^{4} - q^{5} + q^{6} - q^{7} - 3 q^{8} + q^{9} - q^{10} + q^{11} - q^{12} - 2 q^{13} - q^{14} - q^{15} - q^{16} - 2 q^{17} + q^{18} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 