# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("16830.cp1")

sage: E.isogeny_class()

## Elliptic curves in class 16830.cp

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.cp1 16830br2 [1, -1, 1, -347, 2569]  6144
16830.cp2 16830br1 [1, -1, 1, -17, 61]  3072 $$\Gamma_0(N)$$-optimal

## Rank

sage: E.rank()

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

## Modular form 16830.2.a.cp

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 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. 