# Properties

 Label 6336.br Number of curves 3 Conductor 6336 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6336.br1")

sage: E.isogeny_class()

## Elliptic curves in class 6336.br

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6336.br1 6336y3 [0, 0, 0, -281532, 57496282] [] 12000
6336.br2 6336y2 [0, 0, 0, -372, 5002] [] 2400
6336.br3 6336y1 [0, 0, 0, -12, -38] [] 480 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form6336.2.a.br

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrr} 1 & 5 & 25 \\ 5 & 1 & 5 \\ 25 & 5 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.