# Properties

 Label 16830i Number of curves 2 Conductor 16830 CM no Rank 1 Graph # Related objects

Show commands for: SageMath
sage: E = EllipticCurve("16830.k1")
sage: E.isogeny_class()

## Elliptic curves in class 16830i

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
16830.k2 16830i1 [1, -1, 0, -2985, 56141] 2 23040 $$\Gamma_0(N)$$-optimal
16830.k1 16830i2 [1, -1, 0, -46185, 3831821] 2 46080

## Rank

sage: E.rank()

The elliptic curves in class 16830i have rank $$1$$.

## Modular form 16830.2.a.k

sage: E.q_eigenform(10)
$$q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} + q^{11} + q^{16} + q^{17} + 6q^{19} + O(q^{20})$$

## 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 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. 