# Properties

 Label 966.a Number of curves $2$ Conductor $966$ CM no Rank $1$ Graph # Related objects

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

sage: E.isogeny_class()

## Elliptic curves in class 966.a

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
966.a1 966d2 $$[1, 1, 0, -72, -90]$$ $$42180533641/22862322$$ $$22862322$$ $$$$ $$384$$ $$0.10304$$
966.a2 966d1 $$[1, 1, 0, 18, 0]$$ $$590589719/365148$$ $$-365148$$ $$$$ $$192$$ $$-0.24353$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

The elliptic curves in class 966.a do not have complex multiplication.

## Modular form966.2.a.a

sage: E.q_eigenform(10)

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

## 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.

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

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 