# Properties

 Label 32340.bf Number of curves $2$ Conductor $32340$ CM no Rank $1$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("bf1")

sage: E.isogeny_class()

## Elliptic curves in class 32340.bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
32340.bf1 32340bg2 $$[0, 1, 0, -46076, -1485660]$$ $$1047213232/515625$$ $$5326676124000000$$ $$$$ $$161280$$ $$1.7108$$
32340.bf2 32340bg1 $$[0, 1, 0, 10519, -172656]$$ $$199344128/136125$$ $$-87890156046000$$ $$$$ $$80640$$ $$1.3642$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form 32340.2.a.bf

sage: E.q_eigenform(10)

$$q + q^{3} - q^{5} + q^{9} + q^{11} - 2q^{13} - q^{15} + 2q^{17} - 6q^{19} + O(q^{20})$$ ## 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. 