# Properties

 Label 236992.r Number of curves $2$ Conductor $236992$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("r1")

sage: E.isogeny_class()

## Elliptic curves in class 236992.r

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.r1 236992r2 $$[0, 1, 0, -1033313, -404606081]$$ $$12576878500/1127$$ $$10933793384235008$$ $$$$ $$2703360$$ $$2.1176$$
236992.r2 236992r1 $$[0, 1, 0, -59953, -7280529]$$ $$-9826000/3703$$ $$-8981330279907328$$ $$$$ $$1351680$$ $$1.7710$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 236992.r have rank $$1$$.

## Complex multiplication

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

## Modular form 236992.2.a.r

sage: E.q_eigenform(10)

$$q - 2q^{3} + q^{7} + q^{9} + 4q^{11} - 6q^{13} + O(q^{20})$$ ## 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. 