# Properties

 Label 32340.bg Number of curves $2$ Conductor $32340$ CM no Rank $1$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 32340.bg

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.bg1 32340bf2 $$[0, 1, 0, -204836, -33091836]$$ $$31558509702736/2620631475$$ $$78928556134982400$$ $$[2]$$ $$331776$$ $$1.9844$$
32340.bg2 32340bf1 $$[0, 1, 0, 13459, -2355900]$$ $$143225913344/1361505915$$ $$-2562876950301360$$ $$[2]$$ $$165888$$ $$1.6378$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 32340.bg have rank $$1$$.

## Complex multiplication

The elliptic curves in class 32340.bg do not have complex multiplication.

## Modular form 32340.2.a.bg

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} + q^{11} + 2q^{13} - q^{15} + 2q^{17} - 4q^{19} + O(q^{20})$$

## 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.