# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("k1")

sage: E.isogeny_class()

## Elliptic curves in class 8470.k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.k1 8470c1 $$[1, 0, 1, -51549, -4518384]$$ $$-584043889/1400$$ $$-36312394441400$$ $$[]$$ $$38016$$ $$1.4813$$ $$\Gamma_0(N)$$-optimal
8470.k2 8470c2 $$[1, 0, 1, 94861, -22731788]$$ $$3639707951/10718750$$ $$-278016769941968750$$ $$[]$$ $$114048$$ $$2.0306$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8470.2.a.k

sage: E.q_eigenform(10)

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