# Properties

 Label 6336k Number of curves 4 Conductor 6336 CM no Rank 0 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6336.bj1")

sage: E.isogeny_class()

## Elliptic curves in class 6336k

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6336.bj3 6336k1 [0, 0, 0, -3180, -65104] [2] 6144 $$\Gamma_0(N)$$-optimal
6336.bj4 6336k2 [0, 0, 0, 2580, -274768] [2] 12288
6336.bj1 6336k3 [0, 0, 0, -46380, 3829808] [2] 18432
6336.bj2 6336k4 [0, 0, 0, -23340, 7636016] [2] 36864

## Rank

sage: E.rank()

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

## Modular form6336.2.a.bj

sage: E.q_eigenform(10)

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

## 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 Cremona 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 Cremona labels.