# Properties

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

# Related objects

Show commands: SageMath
E = EllipticCurve("k1")

E.isogeny_class()

## Elliptic curves in class 1155.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1155.k1 1155f3 $$[1, 1, 0, -20702, -333459]$$ $$981281029968144361/522287841796875$$ $$522287841796875$$ $$[4]$$ $$4608$$ $$1.5155$$
1155.k2 1155f2 $$[1, 1, 0, -16247, -803016]$$ $$474334834335054841/607815140625$$ $$607815140625$$ $$[2, 2]$$ $$2304$$ $$1.1689$$
1155.k3 1155f1 $$[1, 1, 0, -16242, -803529]$$ $$473897054735271721/779625$$ $$779625$$ $$[2]$$ $$1152$$ $$0.82233$$ $$\Gamma_0(N)$$-optimal
1155.k4 1155f4 $$[1, 1, 0, -11872, -1239641]$$ $$-185077034913624841/551466161890875$$ $$-551466161890875$$ $$[2]$$ $$4608$$ $$1.5155$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form1155.2.a.k

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.