# Properties

 Label 1155m Number of curves $6$ Conductor $1155$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("1155.f1")

sage: E.isogeny_class()

## Elliptic curves in class 1155m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
1155.f6 1155m1 [1, 0, 0, 35, -23128] [4] 960 $$\Gamma_0(N)$$-optimal
1155.f5 1155m2 [1, 0, 0, -11970, -496125] [2, 4] 1920
1155.f2 1155m3 [1, 0, 0, -190575, -32037768] [2, 2] 3840
1155.f4 1155m4 [1, 0, 0, -25445, 821730] [4] 3840
1155.f1 1155m5 [1, 0, 0, -3049200, -2049655293] [2] 7680
1155.f3 1155m6 [1, 0, 0, -189630, -32370975] [2] 7680

## Rank

sage: E.rank()

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

## Modular form1155.2.a.f

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with Cremona labels.