# Properties

 Label 966.i Number of curves $2$ Conductor $966$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("i1")

sage: E.isogeny_class()

## Elliptic curves in class 966.i

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
966.i1 966k2 $$[1, 0, 0, -27, -249]$$ $$-2181825073/25039686$$ $$-25039686$$ $$[]$$ $$360$$ $$0.10160$$
966.i2 966k1 $$[1, 0, 0, 3, 9]$$ $$2924207/34776$$ $$-34776$$ $$$$ $$120$$ $$-0.44771$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form966.2.a.i

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 