# Properties

 Label 16830.v Number of curves 4 Conductor 16830 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("16830.v1")

sage: E.isogeny_class()

## Elliptic curves in class 16830.v

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16830.v1 16830m3 [1, -1, 0, -30039, -1995427] [2] 48384
16830.v2 16830m4 [1, -1, 0, -24639, -2739547] [2] 96768
16830.v3 16830m1 [1, -1, 0, -1164, 12348] [6] 16128 $$\Gamma_0(N)$$-optimal
16830.v4 16830m2 [1, -1, 0, 2586, 73098] [6] 32256

## Rank

sage: E.rank()

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

## Modular form 16830.2.a.v

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrr} 1 & 2 & 3 & 6 \\ 2 & 1 & 6 & 3 \\ 3 & 6 & 1 & 2 \\ 6 & 3 & 2 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.