# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("6336.cd1")

sage: E.isogeny_class()

## Elliptic curves in class 6336.cd

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6336.cd1 6336z3 [0, 0, 0, -17004, -853328]  8192
6336.cd2 6336z2 [0, 0, 0, -1164, -10640] [2, 2] 4096
6336.cd3 6336z1 [0, 0, 0, -444, 3472]  2048 $$\Gamma_0(N)$$-optimal
6336.cd4 6336z4 [0, 0, 0, 3156, -71120]  8192

## Rank

sage: E.rank()

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

## Modular form6336.2.a.cd

sage: E.q_eigenform(10)

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

## 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. 