# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("ce1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.ce

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.ce1 236992ce2 $$[0, -1, 0, -1151809, -461125695]$$ $$1431644/49$$ $$5783976700260319232$$ $$$$ $$3956736$$ $$2.3720$$
236992.ce2 236992ce1 $$[0, -1, 0, -178449, 19130129]$$ $$21296/7$$ $$206570596437868544$$ $$$$ $$1978368$$ $$2.0254$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 236992.2.a.ce

sage: E.q_eigenform(10)

$$q + 2q^{3} - 2q^{5} - q^{7} + q^{9} + 2q^{13} - 4q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$ ## 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 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. 