# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bc1")

sage: E.isogeny_class()

## Elliptic curves in class 8470.bc

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.bc1 8470y2 $$[1, 0, 0, -78477396, -267593527024]$$ $$-249353795628717731809/14000000$$ $$-3001024334000000$$ $$[]$$ $$798336$$ $$2.8844$$
8470.bc2 8470y1 $$[1, 0, 0, -959956, -374215280]$$ $$-456390127585249/17983078400$$ $$-3854832562759270400$$ $$$$ $$266112$$ $$2.3351$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8470.2.a.bc

sage: E.q_eigenform(10)

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