# Properties

 Label 6600.y Number of curves 4 Conductor 6600 CM no Rank 0 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6600.y1")

sage: E.isogeny_class()

## Elliptic curves in class 6600.y

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6600.y1 6600bb3 [0, 1, 0, -11808, 489888]  8192
6600.y2 6600bb2 [0, 1, 0, -808, 5888] [2, 2] 4096
6600.y3 6600bb1 [0, 1, 0, -308, -2112]  2048 $$\Gamma_0(N)$$-optimal
6600.y4 6600bb4 [0, 1, 0, 2192, 41888]  8192

## Rank

sage: E.rank()

The elliptic curves in class 6600.y have rank $$0$$.

## Modular form6600.2.a.y

sage: E.q_eigenform(10)

$$q + q^{3} + q^{9} + q^{11} - 2q^{13} - 6q^{17} + O(q^{20})$$

## 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. 