# Properties

 Label 1155.d Number of curves $4$ Conductor $1155$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("d1")

E.isogeny_class()

## Elliptic curves in class 1155.d

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.d1 1155a3 $$[1, 1, 1, -881, 9698]$$ $$75627935783569/396165$$ $$396165$$ $$[2]$$ $$384$$ $$0.27015$$
1155.d2 1155a2 $$[1, 1, 1, -56, 128]$$ $$19443408769/1334025$$ $$1334025$$ $$[2, 2]$$ $$192$$ $$-0.076428$$
1155.d3 1155a1 $$[1, 1, 1, -11, -16]$$ $$148035889/31185$$ $$31185$$ $$[2]$$ $$96$$ $$-0.42300$$ $$\Gamma_0(N)$$-optimal
1155.d4 1155a4 $$[1, 1, 1, 49, 674]$$ $$12994449551/192163125$$ $$-192163125$$ $$[2]$$ $$384$$ $$0.27015$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1155.2.a.d

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.