# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("966.c1")

sage: E.isogeny_class()

## Elliptic curves in class 966c

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
966.c2 966c1 [1, 1, 0, -14744, 836928]  4224 $$\Gamma_0(N)$$-optimal
966.c1 966c2 [1, 1, 0, -250264, 48082240]  8448

## Rank

sage: E.rank()

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

## Modular form966.2.a.c

sage: E.q_eigenform(10)

$$q - q^{2} - q^{3} + q^{4} + 2q^{5} + q^{6} + q^{7} - q^{8} + q^{9} - 2q^{10} - 4q^{11} - q^{12} - 4q^{13} - q^{14} - 2q^{15} + q^{16} - 4q^{17} - q^{18} - 2q^{19} + O(q^{20})$$

## 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 Cremona 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 Cremona labels. 