# Properties

 Label 189618.bs Number of curves $2$ Conductor $189618$ CM no Rank $1$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("bs1")

sage: E.isogeny_class()

## Elliptic curves in class 189618.bs

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.bs1 189618k2 $$[1, 0, 0, -207282, -20993220]$$ $$204055591784617/78708537864$$ $$379911078938795976$$ $$[2]$$ $$3161088$$ $$2.0722$$
189618.bs2 189618k1 $$[1, 0, 0, -92362, 10563812]$$ $$18052771191337/444958272$$ $$2147728591914048$$ $$[2]$$ $$1580544$$ $$1.7257$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 189618.bs have rank $$1$$.

## Complex multiplication

The elliptic curves in class 189618.bs do not have complex multiplication.

## Modular form 189618.2.a.bs

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + 2q^{5} + q^{6} + 2q^{7} + q^{8} + q^{9} + 2q^{10} - q^{11} + q^{12} + 2q^{14} + 2q^{15} + q^{16} - q^{17} + q^{18} - 6q^{19} + O(q^{20})$$

## 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.