# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("cq1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.cq

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.cq1 236992cq2 $$[0, -1, 0, -796321, -118232127]$$ $$5756278756/2705927$$ $$26252037915548254208$$ $$$$ $$8110080$$ $$2.4205$$
236992.cq2 236992cq1 $$[0, -1, 0, 177039, -14082607]$$ $$253012016/181447$$ $$-440085183715459072$$ $$$$ $$4055040$$ $$2.0739$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 236992.2.a.cq

sage: E.q_eigenform(10)

$$q + 2q^{3} + 4q^{5} + q^{7} + q^{9} - 4q^{11} + 2q^{13} + 8q^{15} + 4q^{17} + O(q^{20})$$ ## 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 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. 