# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("1155.k1")

sage: E.isogeny_class()

## Elliptic curves in class 1155.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1155.k1 1155f3 [1, 1, 0, -20702, -333459]  4608
1155.k2 1155f2 [1, 1, 0, -16247, -803016] [2, 2] 2304
1155.k3 1155f1 [1, 1, 0, -16242, -803529]  1152 $$\Gamma_0(N)$$-optimal
1155.k4 1155f4 [1, 1, 0, -11872, -1239641]  4608

## Rank

sage: E.rank()

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

## Modular form1155.2.a.k

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. 