# Properties

 Label 236992br Number of curves $4$ Conductor $236992$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("br1")

sage: E.isogeny_class()

## Elliptic curves in class 236992br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
236992.br4 236992br1 $$[0, 0, 0, 2116, -194672]$$ $$432/7$$ $$-16977940037632$$ $$$$ $$405504$$ $$1.2191$$ $$\Gamma_0(N)$$-optimal
236992.br3 236992br2 $$[0, 0, 0, -40204, -2920080]$$ $$740772/49$$ $$475382321053696$$ $$[2, 2]$$ $$811008$$ $$1.5657$$
236992.br2 236992br3 $$[0, 0, 0, -124844, 13432368]$$ $$11090466/2401$$ $$46587467463262208$$ $$$$ $$1622016$$ $$1.9123$$
236992.br1 236992br4 $$[0, 0, 0, -632684, -193698640]$$ $$1443468546/7$$ $$135823520301056$$ $$$$ $$1622016$$ $$1.9123$$

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 236992.2.a.br

sage: E.q_eigenform(10)

$$q + 2 q^{5} + q^{7} - 3 q^{9} - 4 q^{11} - 2 q^{13} + 6 q^{17} + 8 q^{19} + O(q^{20})$$ ## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 