# Properties

 Label 189618.q Number of curves $2$ Conductor $189618$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("q1")

sage: E.isogeny_class()

## Elliptic curves in class 189618.q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.q1 189618bb1 $$[1, 0, 1, -33466, 2353496]$$ $$858729462625/38148$$ $$184133109732$$ $$$$ $$552960$$ $$1.2389$$ $$\Gamma_0(N)$$-optimal
189618.q2 189618bb2 $$[1, 0, 1, -31776, 2602264]$$ $$-735091890625/181908738$$ $$-878038733757042$$ $$$$ $$1105920$$ $$1.5855$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 189618.2.a.q

sage: E.q_eigenform(10)

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