# Properties

 Label 236992.cl Number of curves $2$ Conductor $236992$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("cl1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.cl

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.cl1 236992cl2 $$[0, -1, 0, -20500513, 33454460865]$$ $$24553362849625/1755162752$$ $$68112109622265519276032$$ $$$$ $$22708224$$ $$3.1282$$
236992.cl2 236992cl1 $$[0, -1, 0, 1167327, 2283106241]$$ $$4533086375/60669952$$ $$-2354401844896026591232$$ $$$$ $$11354112$$ $$2.7816$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 236992.cl have rank $$0$$.

## Complex multiplication

The elliptic curves in class 236992.cl do not have complex multiplication.

## Modular form 236992.2.a.cl

sage: E.q_eigenform(10)

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