# Properties

 Label 4080.s Number of curves $2$ Conductor $4080$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
E = EllipticCurve("s1")

E.isogeny_class()

## Elliptic curves in class 4080.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
4080.s1 4080ba2 $$[0, 1, 0, -739096, -244794220]$$ $$10901014250685308569/1040774054400$$ $$4263010526822400$$ $$[2]$$ $$48384$$ $$2.0357$$
4080.s2 4080ba1 $$[0, 1, 0, -42776, -4424556]$$ $$-2113364608155289/828431400960$$ $$-3393255018332160$$ $$[2]$$ $$24192$$ $$1.6892$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form4080.2.a.s

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} - 2 q^{7} + q^{9} + 4 q^{11} + 4 q^{13} - q^{15} + q^{17} + 4 q^{19} + O(q^{20})$$

## 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.