# Properties

 Label 166410.b Number of curves $2$ Conductor $166410$ CM no Rank $1$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 166410.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
166410.b1 166410bz2 $$[1, -1, 0, -16020, -909104]$$ $$-337335507529/72000000$$ $$-97050312000000$$ $$[]$$ $$580608$$ $$1.4052$$
166410.b2 166410bz1 $$[1, -1, 0, 1395, 6925]$$ $$222641831/145800$$ $$-196526881800$$ $$[]$$ $$193536$$ $$0.85585$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 166410.b have rank $$1$$.

## Complex multiplication

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

## Modular form 166410.2.a.b

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - 2q^{7} - q^{8} + q^{10} + 3q^{11} - 4q^{13} + 2q^{14} + q^{16} + 3q^{17} + q^{19} + O(q^{20})$$ ## 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. 