# Properties

 Label 199920ch Number of curves $2$ Conductor $199920$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ch1")

sage: E.isogeny_class()

## Elliptic curves in class 199920ch

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
199920.cv2 199920ch1 $$[0, -1, 0, 63880, 7398000]$$ $$59822347031/83966400$$ $$-40462594021785600$$ $$[2]$$ $$1327104$$ $$1.8722$$ $$\Gamma_0(N)$$-optimal
199920.cv1 199920ch2 $$[0, -1, 0, -406520, 73630320]$$ $$15417797707369/4080067320$$ $$1966144881175265280$$ $$[2]$$ $$2654208$$ $$2.2188$$

## Rank

sage: E.rank()

The elliptic curves in class 199920ch have rank $$0$$.

## Complex multiplication

The elliptic curves in class 199920ch do not have complex multiplication.

## Modular form 199920.2.a.ch

sage: E.q_eigenform(10)

$$q - q^{3} + q^{5} + q^{9} - 2q^{11} + 2q^{13} - q^{15} - q^{17} - 4q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels.