# Properties

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

Show commands for: SageMath
sage: E = EllipticCurve("16830.f1")

sage: E.isogeny_class()

## Elliptic curves in class 16830p

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.f1 16830p1 [1, -1, 0, -21958515, -39645067019] [] 1440000 $$\Gamma_0(N)$$-optimal
16830.f2 16830p2 [1, -1, 0, 155552085, 462972313741] [] 7200000

## Rank

sage: E.rank()

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

## Modular form 16830.2.a.f

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rr} 1 & 5 \\ 5 & 1 \end{array}\right)$$

## Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with Cremona labels. 