# Properties

 Label 2880bg Number of curves 4 Conductor 2880 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2880.bg1")

sage: E.isogeny_class()

## Elliptic curves in class 2880bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.bg3 2880bg1 [0, 0, 0, -72, 216]  512 $$\Gamma_0(N)$$-optimal
2880.bg2 2880bg2 [0, 0, 0, -252, -1296] [2, 2] 1024
2880.bg1 2880bg3 [0, 0, 0, -3852, -92016]  2048
2880.bg4 2880bg4 [0, 0, 0, 468, -7344]  2048

## Rank

sage: E.rank()

The elliptic curves in class 2880bg have rank $$0$$.

## Modular form2880.2.a.bg

sage: E.q_eigenform(10)

$$q + q^{5} + 4q^{7} - 4q^{11} + 2q^{13} - 2q^{17} + 4q^{19} + O(q^{20})$$

## 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 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. 