# Properties

 Label 966f Number of curves $4$ Conductor $966$ CM no Rank $0$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("966.f1")

sage: E.isogeny_class()

## Elliptic curves in class 966f

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
966.f4 966f1 [1, 0, 1, 4644, 858394] [6] 4800 $$\Gamma_0(N)$$-optimal
966.f2 966f2 [1, 0, 1, -111996, 13735450] [6] 9600
966.f3 966f3 [1, 0, 1, -41931, -23576714] [2] 14400
966.f1 966f4 [1, 0, 1, -1516491, -715440266] [2] 28800

## Rank

sage: E.rank()

The elliptic curves in class 966f have rank $$0$$.

## Modular form966.2.a.f

sage: E.q_eigenform(10)

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

## 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 Cremona numbering.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with Cremona labels.