# Properties

 Label 206400.bg Number of curves $2$ Conductor $206400$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bg1")

sage: E.isogeny_class()

## Elliptic curves in class 206400.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
206400.bg1 206400ed2 $$[0, -1, 0, -380033, 87419937]$$ $$1481933914201/53916840$$ $$220843376640000000$$ $$$$ $$2654208$$ $$2.0977$$
206400.bg2 206400ed1 $$[0, -1, 0, -60033, -3780063]$$ $$5841725401/1857600$$ $$7608729600000000$$ $$$$ $$1327104$$ $$1.7512$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 206400.bg have rank $$1$$.

## Complex multiplication

The elliptic curves in class 206400.bg do not have complex multiplication.

## Modular form 206400.2.a.bg

sage: E.q_eigenform(10)

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