# Properties

 Label 1155.e Number of curves $6$ Conductor $1155$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("e1")

E.isogeny_class()

## Elliptic curves in class 1155.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.e1 1155e5 $$[1, 1, 1, -13250, -592540]$$ $$257260669489908001/14267882475$$ $$14267882475$$ $$[2]$$ $$2048$$ $$1.0139$$
1155.e2 1155e3 $$[1, 1, 1, -875, -8440]$$ $$74093292126001/14707625625$$ $$14707625625$$ $$[2, 2]$$ $$1024$$ $$0.66729$$
1155.e3 1155e2 $$[1, 1, 1, -270, 1482]$$ $$2177286259681/161417025$$ $$161417025$$ $$[2, 4]$$ $$512$$ $$0.32072$$
1155.e4 1155e1 $$[1, 1, 1, -265, 1550]$$ $$2058561081361/12705$$ $$12705$$ $$[4]$$ $$256$$ $$-0.025854$$ $$\Gamma_0(N)$$-optimal
1155.e5 1155e4 $$[1, 1, 1, 255, 7152]$$ $$1833318007919/22507682505$$ $$-22507682505$$ $$[4]$$ $$1024$$ $$0.66729$$
1155.e6 1155e6 $$[1, 1, 1, 1820, -47248]$$ $$666688497209279/1381398046875$$ $$-1381398046875$$ $$[2]$$ $$2048$$ $$1.0139$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1155.2.a.e

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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 4 & 8 & 8 & 4 \\ 2 & 1 & 2 & 4 & 4 & 2 \\ 4 & 2 & 1 & 2 & 2 & 4 \\ 8 & 4 & 2 & 1 & 4 & 8 \\ 8 & 4 & 2 & 4 & 1 & 8 \\ 4 & 2 & 4 & 8 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.