# Properties

 Label 966.g Number of curves $6$ Conductor $966$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("966.g1")

sage: E.isogeny_class()

## Elliptic curves in class 966.g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
966.g1 966g5 [1, 1, 1, -79134, -8601153] [2] 4096
966.g2 966g4 [1, 1, 1, -17714, 900047] [8] 2048
966.g3 966g3 [1, 1, 1, -5074, -128689] [2, 2] 2048
966.g4 966g2 [1, 1, 1, -1154, 12431] [2, 4] 1024
966.g5 966g1 [1, 1, 1, 126, 1167] [4] 512 $$\Gamma_0(N)$$-optimal
966.g6 966g6 [1, 1, 1, 6266, -609505] [2] 4096

## Rank

sage: E.rank()

The elliptic curves in class 966.g have rank $$1$$.

## Modular form966.2.a.g

sage: E.q_eigenform(10)

$$q + q^{2} - q^{3} + q^{4} - 2q^{5} - q^{6} + q^{7} + q^{8} + q^{9} - 2q^{10} - 4q^{11} - q^{12} - 2q^{13} + q^{14} + 2q^{15} + q^{16} - 6q^{17} + q^{18} + 4q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 2 & 4 & 8 & 4 \\ 8 & 1 & 4 & 2 & 4 & 8 \\ 2 & 4 & 1 & 2 & 4 & 2 \\ 4 & 2 & 2 & 1 & 2 & 4 \\ 8 & 4 & 4 & 2 & 1 & 8 \\ 4 & 8 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.