# Properties

 Label 6336.bf Number of curves $4$ Conductor $6336$ CM no Rank $0$ Graph

# Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 6336.bf

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
6336.bf1 6336ce3 $$[0, 0, 0, -46380, -3829808]$$ $$57736239625/255552$$ $$48836747722752$$ $$[2]$$ $$18432$$ $$1.4790$$
6336.bf2 6336ce4 $$[0, 0, 0, -23340, -7636016]$$ $$-7357983625/127552392$$ $$-24375641707118592$$ $$[2]$$ $$36864$$ $$1.8255$$
6336.bf3 6336ce1 $$[0, 0, 0, -3180, 65104]$$ $$18609625/1188$$ $$227030335488$$ $$[2]$$ $$6144$$ $$0.92964$$ $$\Gamma_0(N)$$-optimal
6336.bf4 6336ce2 $$[0, 0, 0, 2580, 274768]$$ $$9938375/176418$$ $$-33714004819968$$ $$[2]$$ $$12288$$ $$1.2762$$

## Rank

sage: E.rank()

The elliptic curves in class 6336.bf have rank $$0$$.

## Complex multiplication

The elliptic curves in class 6336.bf do not have complex multiplication.

## Modular form6336.2.a.bf

sage: E.q_eigenform(10)

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

## 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 LMFDB numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.