# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("1155.l1")

sage: E.isogeny_class()

## Elliptic curves in class 1155.l

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1155.l1 1155h3 [1, 0, 1, -2054, -35989]  384
1155.l2 1155h4 [1, 0, 1, -204, 151]  384
1155.l3 1155h2 [1, 0, 1, -129, -569] [2, 2] 192
1155.l4 1155h1 [1, 0, 1, -4, -19]  96 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form1155.2.a.l

sage: E.q_eigenform(10)

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

## 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. 