# Properties

 Label 11154bf Number of curves 4 Conductor 11154 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("11154.bg1")

sage: E.isogeny_class()

## Elliptic curves in class 11154bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
11154.bg3 11154bf1 [1, 0, 0, -933, 10269]  8640 $$\Gamma_0(N)$$-optimal
11154.bg4 11154bf2 [1, 0, 0, 757, 43731]  17280
11154.bg1 11154bf3 [1, 0, 0, -13608, -609792]  25920
11154.bg2 11154bf4 [1, 0, 0, -6848, -1214136]  51840

## Rank

sage: E.rank()

The elliptic curves in class 11154bf have rank $$0$$.

## Modular form 11154.2.a.bg

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels. 