# Properties

 Label 2070.g Number of curves $2$ Conductor $2070$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 2070.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
2070.g1 2070g2 $$[1, -1, 0, -7074, 160380]$$ $$53706380371489/16171875000$$ $$11789296875000$$ $$$$ $$3840$$ $$1.2134$$
2070.g2 2070g1 $$[1, -1, 0, 1206, 16308]$$ $$265971760991/317400000$$ $$-231384600000$$ $$$$ $$1920$$ $$0.86683$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 2070.g have rank $$1$$.

## Complex multiplication

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

## Modular form2070.2.a.g

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} - q^{8} - q^{10} - 2 q^{11} + q^{16} - 6 q^{17} + 4 q^{19} + O(q^{20})$$

## 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. 