# Properties

 Label 6336.x Number of curves 4 Conductor 6336 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6336.x1")

sage: E.isogeny_class()

## Elliptic curves in class 6336.x

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6336.x1 6336bd3 [0, 0, 0, -84396, -9427664]  24576
6336.x2 6336bd2 [0, 0, 0, -6636, -65360] [2, 2] 12288
6336.x3 6336bd1 [0, 0, 0, -3756, 87856]  6144 $$\Gamma_0(N)$$-optimal
6336.x4 6336bd4 [0, 0, 0, 25044, -508880]  24576

## Rank

sage: E.rank()

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

## Modular form6336.2.a.x

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 