# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("966.e1")

sage: E.isogeny_class()

## Elliptic curves in class 966.e

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
966.e1 966e2 [1, 0, 1, -361, 2564]  384
966.e2 966e1 [1, 0, 1, -1, 116]  192 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## 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. 