# Properties

 Label 16830q Number of curves 2 Conductor 16830 CM no Rank 2 Graph

# Learn more about

Show commands for: SageMath
sage: E = EllipticCurve("16830.e1")

sage: E.isogeny_class()

## Elliptic curves in class 16830q

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.e2 16830q1 [1, -1, 0, -1800, 25600] [2] 18432 $$\Gamma_0(N)$$-optimal
16830.e1 16830q2 [1, -1, 0, -7920, -244904] [2] 36864

## Rank

sage: E.rank()

The elliptic curves in class 16830q have rank $$2$$.

## Modular form 16830.2.a.e

sage: E.q_eigenform(10)

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

## 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 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.