# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("16830.a1")
sage: E.isogeny_class()

## Elliptic curves in class 16830.a

sage: E.isogeny_class().curves
LMFDB label Cremona label Weierstrass coefficients Torsion order Modular degree Optimality
16830.a1 16830d1 [1, -1, 0, -249330, -47842924] 2 153600 $$\Gamma_0(N)$$-optimal
16830.a2 16830d2 [1, -1, 0, -214650, -61652500] 2 307200

## Rank

sage: E.rank()

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

## Modular form 16830.2.a.a

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

## 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. 