# Properties

 Label 2070.s Number of curves $2$ Conductor $2070$ CM no Rank $0$ Graph # Learn more about

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

sage: E.isogeny_class()

## Elliptic curves in class 2070.s

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.s1 2070r2 $$[1, -1, 1, -6782, 96981]$$ $$47316161414809/22001657400$$ $$16039208244600$$ $$$$ $$5376$$ $$1.2284$$
2070.s2 2070r1 $$[1, -1, 1, 1498, 10869]$$ $$510273943271/370215360$$ $$-269886997440$$ $$$$ $$2688$$ $$0.88179$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2070.s have rank $$0$$.

## Complex multiplication

The elliptic curves in class 2070.s do not have complex multiplication.

## Modular form2070.2.a.s

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} + 4q^{7} + q^{8} + q^{10} + 2q^{11} + 4q^{14} + q^{16} - 2q^{17} + O(q^{20})$$ ## 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. 