# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("16830.j1")

sage: E.isogeny_class()

## Elliptic curves in class 16830g

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.j2 16830g1 [1, -1, 0, -150, -1504]  9216 $$\Gamma_0(N)$$-optimal
16830.j1 16830g2 [1, -1, 0, -3120, -66250]  18432

## Rank

sage: E.rank()

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

## Modular form 16830.2.a.j

sage: E.q_eigenform(10)

$$q - q^{2} + q^{4} - q^{5} - q^{8} + q^{10} - q^{11} + 6q^{13} + q^{16} + q^{17} - 4q^{19} + O(q^{20})$$

## 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. 