# Properties

 Label 8470.v Number of curves $2$ Conductor $8470$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("v1")

sage: E.isogeny_class()

## Elliptic curves in class 8470.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.v1 8470bg2 $$[1, 0, 0, -102550, -12089868]$$ $$67324767141241/3368750000$$ $$5967946118750000$$ $$$$ $$61440$$ $$1.7858$$
8470.v2 8470bg1 $$[1, 0, 0, 3930, -739100]$$ $$3789119879/135520000$$ $$-240081946720000$$ $$$$ $$30720$$ $$1.4393$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8470.v have rank $$1$$.

## Complex multiplication

The elliptic curves in class 8470.v do not have complex multiplication.

## Modular form8470.2.a.v

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} + q^{5} - 2q^{6} + q^{7} + q^{8} + q^{9} + q^{10} - 2q^{12} + q^{14} - 2q^{15} + q^{16} + q^{18} + O(q^{20})$$ ## 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. 