# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("1155.d1")

sage: E.isogeny_class()

## Elliptic curves in class 1155a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1155.d3 1155a1 [1, 1, 1, -11, -16]  96 $$\Gamma_0(N)$$-optimal
1155.d2 1155a2 [1, 1, 1, -56, 128] [2, 2] 192
1155.d1 1155a3 [1, 1, 1, -881, 9698]  384
1155.d4 1155a4 [1, 1, 1, 49, 674]  384

## Rank

sage: E.rank()

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

## Modular form1155.2.a.d

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels. 