# Properties

 Label 16830ck Number of curves $2$ Conductor $16830$ CM no Rank $0$ Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("ck1")

sage: E.isogeny_class()

## Elliptic curves in class 16830ck

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.cd2 16830ck1 [1, -1, 1, 238, -1299]  8192 $$\Gamma_0(N)$$-optimal
16830.cd1 16830ck2 [1, -1, 1, -1292, -11091]  16384

## Rank

sage: E.rank()

The elliptic curves in class 16830ck have rank $$0$$.

## Complex multiplication

The elliptic curves in class 16830ck do not have complex multiplication.

## Modular form 16830.2.a.ck

sage: E.q_eigenform(10)

$$q + q^{2} + q^{4} + q^{5} - 2q^{7} + q^{8} + q^{10} - q^{11} - 2q^{14} + q^{16} - q^{17} + O(q^{20})$$

## 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. 