# Properties

 Label 189618.o Number of curves $2$ Conductor $189618$ CM no Rank $0$ Graph # Learn more

Show commands: SageMath
sage: E = EllipticCurve("o1")

sage: E.isogeny_class()

## Elliptic curves in class 189618.o

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.o1 189618y2 $$[1, 0, 1, -30762, 2073970]$$ $$666940371553/37026$$ $$178717430034$$ $$$$ $$414720$$ $$1.2245$$
189618.o2 189618y1 $$[1, 0, 1, -2032, 28394]$$ $$192100033/38148$$ $$184133109732$$ $$$$ $$207360$$ $$0.87789$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 189618.o have rank $$0$$.

## Complex multiplication

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

## Modular form 189618.2.a.o

sage: E.q_eigenform(10)

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