# Properties

 Label 166410.bf Number of curves $2$ Conductor $166410$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bf1")

sage: E.isogeny_class()

## Elliptic curves in class 166410.bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166410.bf1 166410bs2 $$[1, -1, 0, -3952584, -2927003720]$$ $$1481933914201/53916840$$ $$248463553749142121640$$ $$[2]$$ $$8515584$$ $$2.6832$$
166410.bf2 166410bs1 $$[1, -1, 0, -624384, 127618240]$$ $$5841725401/1857600$$ $$8560329155870529600$$ $$[2]$$ $$4257792$$ $$2.3366$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 166410.bf have rank $$0$$.

## Complex multiplication

The elliptic curves in class 166410.bf do not have complex multiplication.

## Modular form 166410.2.a.bf

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} + q^{5} + 2q^{7} - q^{8} - q^{10} + 2q^{11} - 2q^{13} - 2q^{14} + q^{16} + 4q^{17} + 6q^{19} + O(q^{20})$$

## 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.