# Properties

 Label 2880ba Number of curves 4 Conductor 2880 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("2880.f1")

sage: E.isogeny_class()

## Elliptic curves in class 2880ba

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
2880.f3 2880ba1 [0, 0, 0, -48, 88]  384 $$\Gamma_0(N)$$-optimal
2880.f4 2880ba2 [0, 0, 0, 132, 592]  768
2880.f1 2880ba3 [0, 0, 0, -1488, -22088]  1152
2880.f2 2880ba4 [0, 0, 0, -1308, -27632]  2304

## Rank

sage: E.rank()

The elliptic curves in class 2880ba have rank $$1$$.

## Modular form2880.2.a.f

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. 