# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("p1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.p1 236992p2 $$[0, 1, 0, -35904993, 12061596319]$$ $$263822189935250/149429406721$$ $$2899432579620642484256768$$ $$$$ $$32440320$$ $$3.3838$$
236992.p2 236992p1 $$[0, 1, 0, 8869567, 1503755071]$$ $$7953970437500/4703287687$$ $$-45629792188353658421248$$ $$$$ $$16220160$$ $$3.0373$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 236992.2.a.p

sage: E.q_eigenform(10)

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