# Properties

 Label 1155.d 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 1155.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
1155.d1 1155a3 [1, 1, 1, -881, 9698] 2 384
1155.d2 1155a2 [1, 1, 1, -56, 128] 4 192
1155.d3 1155a1 [1, 1, 1, -11, -16] 2 96 $$\Gamma_0(N)$$-optimal
1155.d4 1155a4 [1, 1, 1, 49, 674] 2 384

## Rank

sage: E.rank()

The elliptic curves in class 1155.d 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 LMFDB 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 LMFDB labels. 