# Properties

 Label 189618.m Number of curves $2$ Conductor $189618$ CM no Rank $0$ Graph

# Related objects

Show commands: SageMath
sage: E = EllipticCurve("m1")

sage: E.isogeny_class()

## Elliptic curves in class 189618.m

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.m1 189618w1 $$[1, 0, 1, -33128, -2322058]$$ $$832972004929/610368$$ $$2946129755712$$ $$[2]$$ $$903168$$ $$1.3268$$ $$\Gamma_0(N)$$-optimal
189618.m2 189618w2 $$[1, 0, 1, -26368, -3295498]$$ $$-420021471169/727634952$$ $$-3512154935028168$$ $$[2]$$ $$1806336$$ $$1.6734$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 189618.2.a.m

sage: E.q_eigenform(10)

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

## 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.