# Properties

 Label 8470.u Number of curves $2$ Conductor $8470$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("u1")

sage: E.isogeny_class()

## Elliptic curves in class 8470.u

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.u1 8470bc2 $$[1, 0, 0, -366330, 85315132]$$ $$-209611155721/13720$$ $$-355861465525720$$ $$[]$$ $$71280$$ $$1.8487$$
8470.u2 8470bc1 $$[1, 0, 0, -305, 324127]$$ $$-121/1750$$ $$-45390493051750$$ $$[]$$ $$23760$$ $$1.2994$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 8470.u have rank $$0$$.

## Complex multiplication

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

## Modular form8470.2.a.u

sage: E.q_eigenform(10)

$$q + q^{2} - 2q^{3} + q^{4} + q^{5} - 2q^{6} - q^{7} + q^{8} + q^{9} + q^{10} - 2q^{12} - 2q^{13} - q^{14} - 2q^{15} + q^{16} - 3q^{17} + q^{18} + q^{19} + O(q^{20})$$ ## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 