# Properties

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

Show commands: SageMath
sage: E = EllipticCurve("e1")

sage: E.isogeny_class()

## Elliptic curves in class 966.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
966.e1 966e2 $$[1, 0, 1, -361, 2564]$$ $$5182207647625/91449288$$ $$91449288$$ $$$$ $$384$$ $$0.32385$$
966.e2 966e1 $$[1, 0, 1, -1, 116]$$ $$-15625/5842368$$ $$-5842368$$ $$$$ $$192$$ $$-0.022728$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form966.2.a.e

sage: E.q_eigenform(10)

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