# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("16830.d1")
sage: E.isogeny_class()

## Elliptic curves in class 16830.d

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
16830.d1 16830e1 [1, -1, 0, -1171410, 170143316] 2 748800 $$\Gamma_0(N)$$-optimal
16830.d2 16830e2 [1, -1, 0, 4358190, 1312558676] 2 1497600

## Rank

sage: E.rank()

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

## Modular form 16830.2.a.d

sage: E.q_eigenform(10)
$$q - q^{2} + q^{4} - q^{5} - 4q^{7} - q^{8} + q^{10} - q^{11} + 6q^{13} + 4q^{14} + q^{16} - q^{17} - 2q^{19} + O(q^{20})$$

## 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 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. 