# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("6336.n1")

sage: E.isogeny_class()

## Elliptic curves in class 6336.n

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6336.n1 6336cc3 [0, 0, 0, -84396, 9427664]  24576
6336.n2 6336cc2 [0, 0, 0, -6636, 65360] [2, 2] 12288
6336.n3 6336cc1 [0, 0, 0, -3756, -87856]  6144 $$\Gamma_0(N)$$-optimal
6336.n4 6336cc4 [0, 0, 0, 25044, 508880]  24576

## Rank

sage: E.rank()

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

## Modular form6336.2.a.n

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. 