# Properties

 Label 1155c Number of curves $4$ Conductor $1155$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1155.j1")

sage: E.isogeny_class()

## Elliptic curves in class 1155c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1155.j3 1155c1 [1, 1, 0, -203, 1032]  288 $$\Gamma_0(N)$$-optimal
1155.j2 1155c2 [1, 1, 0, -248, 483] [2, 2] 576
1155.j1 1155c3 [1, 1, 0, -2123, -38142]  1152
1155.j4 1155c4 [1, 1, 0, 907, 4872]  1152

## Rank

sage: E.rank()

The elliptic curves in class 1155c have rank $$0$$.

## Modular form1155.2.a.j

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 Cremona 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 Cremona labels. 