# Properties

 Label 162288.bg Number of curves $6$ Conductor $162288$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("162288.bg1")

sage: E.isogeny_class()

## Elliptic curves in class 162288.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
162288.bg1 162288o5 [0, 0, 0, -558369651, 5078394744626] [2] 37748736
162288.bg2 162288o4 [0, 0, 0, -124990131, -537836216974] [2] 18874368
162288.bg3 162288o3 [0, 0, 0, -35802291, 75021299570] [2, 2] 18874368
162288.bg4 162288o2 [0, 0, 0, -8142771, -7653005710] [2, 2] 9437184
162288.bg5 162288o1 [0, 0, 0, 888909, -660679054] [2] 4718592 $$\Gamma_0(N)$$-optimal
162288.bg6 162288o6 [0, 0, 0, 44212749, 362803392434] [2] 37748736

## Rank

sage: E.rank()

The elliptic curves in class 162288.bg have rank $$0$$.

## Modular form 162288.2.a.bg

sage: E.q_eigenform(10)

$$q - 2q^{5} - 4q^{11} + 2q^{13} - 6q^{17} + 4q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.