# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("2880.m1")

sage: E.isogeny_class()

## Elliptic curves in class 2880i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.m3 2880i1 [0, 0, 0, -48, -88]  384 $$\Gamma_0(N)$$-optimal
2880.m4 2880i2 [0, 0, 0, 132, -592]  768
2880.m1 2880i3 [0, 0, 0, -1488, 22088]  1152
2880.m2 2880i4 [0, 0, 0, -1308, 27632]  2304

## Rank

sage: E.rank()

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

## Modular form2880.2.a.m

sage: E.q_eigenform(10)

$$q - q^{5} + 2q^{7} - 2q^{13} + 6q^{17} + 4q^{19} + O(q^{20})$$

## 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 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. 