# Properties

 Label 6336ca Number of curves 2 Conductor 6336 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6336.cg1")

sage: E.isogeny_class()

## Elliptic curves in class 6336ca

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6336.cg2 6336ca1 [0, 0, 0, 96, -200]  1536 $$\Gamma_0(N)$$-optimal
6336.cg1 6336ca2 [0, 0, 0, -444, -1712]  3072

## Rank

sage: E.rank()

The elliptic curves in class 6336ca have rank $$1$$.

## Modular form6336.2.a.cg

sage: E.q_eigenform(10)

$$q + 2q^{5} + 2q^{7} - q^{11} + 2q^{13} - 4q^{17} - 6q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 