# Properties

 Label 28050.bg Number of curves 6 Conductor 28050 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("28050.bg1")

sage: E.isogeny_class()

## Elliptic curves in class 28050.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
28050.bg1 28050y6 [1, 0, 1, -7303501, -7596749602] [2] 1179648
28050.bg2 28050y4 [1, 0, 1, -497251, -96262102] [2, 2] 589824
28050.bg3 28050y2 [1, 0, 1, -184751, 29362898] [2, 2] 294912
28050.bg4 28050y1 [1, 0, 1, -182751, 30054898] [2] 147456 $$\Gamma_0(N)$$-optimal
28050.bg5 28050y3 [1, 0, 1, 95749, 110707898] [2] 589824
28050.bg6 28050y5 [1, 0, 1, 1308999, -634524602] [2] 1179648

## Rank

sage: E.rank()

The elliptic curves in class 28050.bg have rank $$0$$.

## Modular form 28050.2.a.bg

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels.