# Properties

 Label 966.j Number of curves $4$ Conductor $966$ CM no Rank $0$ Graph # Related objects

Show commands: SageMath
sage: E = EllipticCurve("j1")

sage: E.isogeny_class()

## Elliptic curves in class 966.j

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
966.j1 966i3 $$[1, 0, 0, -178849, -29127301]$$ $$632678989847546725777/80515134$$ $$80515134$$ $$$$ $$3840$$ $$1.3770$$
966.j2 966i4 $$[1, 0, 0, -12789, -316305]$$ $$231331938231569617/90942310746882$$ $$90942310746882$$ $$$$ $$3840$$ $$1.3770$$
966.j3 966i2 $$[1, 0, 0, -11179, -455731]$$ $$154502321244119857/55101928644$$ $$55101928644$$ $$[2, 2]$$ $$1920$$ $$1.0304$$
966.j4 966i1 $$[1, 0, 0, -599, -9255]$$ $$-23771111713777/22848457968$$ $$-22848457968$$ $$$$ $$960$$ $$0.68384$$ $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Complex multiplication

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

## Modular form966.2.a.j

sage: E.q_eigenform(10)

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

$$\left(\begin{array}{rrrr} 1 & 4 & 2 & 4 \\ 4 & 1 & 2 & 4 \\ 2 & 2 & 1 & 2 \\ 4 & 4 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels. 