# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("bb1")

sage: E.isogeny_class()

## Elliptic curves in class 8470.bb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
8470.bb1 8470r1 $$[1, 0, 0, -41, -175]$$ $$-63088729/68600$$ $$-8300600$$ $$[]$$ $$1728$$ $$0.022461$$ $$\Gamma_0(N)$$-optimal
8470.bb2 8470r2 $$[1, 0, 0, 344, 3136]$$ $$37199299511/56000000$$ $$-6776000000$$ $$[]$$ $$5184$$ $$0.57177$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form8470.2.a.bb

sage: E.q_eigenform(10)

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