# Properties

 Label 2880.f Number of curves $4$ Conductor $2880$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2880.f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.f1 2880ba3 $$[0, 0, 0, -1488, -22088]$$ $$488095744/125$$ $$93312000$$ $$[2]$$ $$1152$$ $$0.51524$$
2880.f2 2880ba4 $$[0, 0, 0, -1308, -27632]$$ $$-20720464/15625$$ $$-186624000000$$ $$[2]$$ $$2304$$ $$0.86181$$
2880.f3 2880ba1 $$[0, 0, 0, -48, 88]$$ $$16384/5$$ $$3732480$$ $$[2]$$ $$384$$ $$-0.034070$$ $$\Gamma_0(N)$$-optimal
2880.f4 2880ba2 $$[0, 0, 0, 132, 592]$$ $$21296/25$$ $$-298598400$$ $$[2]$$ $$768$$ $$0.31250$$

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 2880.f do not have complex multiplication.

## 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 LMFDB 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 LMFDB labels.