# Properties

 Label 189618.g Number of curves $2$ Conductor $189618$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("g1")

sage: E.isogeny_class()

## Elliptic curves in class 189618.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
189618.g1 189618bo1 $$[1, 1, 0, -14253125, -20716222899]$$ $$66342819962001390625/4812668669952$$ $$23229832450142343168$$ $$$$ $$9934848$$ $$2.7672$$ $$\Gamma_0(N)$$-optimal
189618.g2 189618bo2 $$[1, 1, 0, -13333765, -23503170803]$$ $$-54315282059491182625/17983956399469632$$ $$-86805122604567614964288$$ $$$$ $$19869696$$ $$3.1137$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 189618.2.a.g

sage: E.q_eigenform(10)

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