# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 8470.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.bg1 8470t2 $$[1, 1, 1, -8896, 318979]$$ $$43949604889/42350$$ $$75025608350$$ $$$$ $$15360$$ $$1.0079$$
8470.bg2 8470t1 $$[1, 1, 1, -426, 7283]$$ $$-4826809/10780$$ $$-19097427580$$ $$$$ $$7680$$ $$0.66136$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8470.2.a.bg

sage: E.q_eigenform(10)

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