# Properties

 Label 229320ck Number of curves $2$ Conductor $229320$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("ck1")

sage: E.isogeny_class()

## Elliptic curves in class 229320ck

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
229320.l2 229320ck1 $$[0, 0, 0, -25350003, -85794962498]$$ $$-553867390580563692/657061767578125$$ $$-2137263940743750000000000$$ $$$$ $$31997952$$ $$3.3624$$ $$\Gamma_0(N)$$-optimal
229320.l1 229320ck2 $$[0, 0, 0, -484725003, -4105969337498]$$ $$1936101054887046531846/905403781953125$$ $$5890121600329905120000000$$ $$$$ $$63995904$$ $$3.7089$$

## Rank

sage: E.rank()

The elliptic curves in class 229320ck have rank $$0$$.

## Complex multiplication

The elliptic curves in class 229320ck do not have complex multiplication.

## Modular form 229320.2.a.ck

sage: E.q_eigenform(10)

$$q - q^{5} - 4q^{11} + q^{13} - 6q^{17} + O(q^{20})$$ ## 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. 