# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("b1")

sage: E.isogeny_class()

## Elliptic curves in class 966.b

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
966.b1 966a2 $$[1, 1, 0, -3346, 63700]$$ $$4144806984356137/568114785504$$ $$568114785504$$ $$$$ $$1920$$ $$0.98234$$
966.b2 966a1 $$[1, 1, 0, 334, 5556]$$ $$4101378352343/15049939968$$ $$-15049939968$$ $$$$ $$960$$ $$0.63576$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form966.2.a.b

sage: E.q_eigenform(10)

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