# Properties

 Label 6600.a Number of curves 4 Conductor 6600 CM no Rank 2 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("6600.a1")

sage: E.isogeny_class()

## Elliptic curves in class 6600.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
6600.a1 6600v4 [0, -1, 0, -17608, 905212]  12288
6600.a2 6600v3 [0, -1, 0, -2608, -30788]  12288
6600.a3 6600v2 [0, -1, 0, -1108, 14212] [2, 2] 6144
6600.a4 6600v1 [0, -1, 0, 17, 712]  3072 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

The elliptic curves in class 6600.a have rank $$2$$.

## Modular form6600.2.a.a

sage: E.q_eigenform(10)

$$q - q^{3} - 4q^{7} + q^{9} - q^{11} - 6q^{13} - 6q^{17} - 8q^{19} + O(q^{20})$$

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 