# Properties

 Label 2880.m Number of curves $4$ Conductor $2880$ CM no Rank $0$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 2880.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2880.m1 2880i3 $$[0, 0, 0, -1488, 22088]$$ $$488095744/125$$ $$93312000$$ $$$$ $$1152$$ $$0.51524$$
2880.m2 2880i4 $$[0, 0, 0, -1308, 27632]$$ $$-20720464/15625$$ $$-186624000000$$ $$$$ $$2304$$ $$0.86181$$
2880.m3 2880i1 $$[0, 0, 0, -48, -88]$$ $$16384/5$$ $$3732480$$ $$$$ $$384$$ $$-0.034070$$ $$\Gamma_0(N)$$-optimal
2880.m4 2880i2 $$[0, 0, 0, 132, -592]$$ $$21296/25$$ $$-298598400$$ $$$$ $$768$$ $$0.31250$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## 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 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. 