# Properties

 Label 4080.n Number of curves $2$ Conductor $4080$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
E = EllipticCurve("n1")

E.isogeny_class()

## Elliptic curves in class 4080.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4080.n1 4080w2 $$[0, -1, 0, -185640, 30848112]$$ $$172735174415217961/39657600$$ $$162437529600$$ $$$$ $$16128$$ $$1.5318$$
4080.n2 4080w1 $$[0, -1, 0, -11560, 488560]$$ $$-41713327443241/639221760$$ $$-2618252328960$$ $$$$ $$8064$$ $$1.1853$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 4080.n have rank $$0$$.

## Complex multiplication

The elliptic curves in class 4080.n do not have complex multiplication.

## Modular form4080.2.a.n

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + 2 q^{7} + q^{9} - 4 q^{11} - q^{15} + q^{17} - 4 q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 