# Properties

 Label 16562.bv Number of curves 6 Conductor 16562 CM no Rank 1 Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("16562.bv1")

sage: E.isogeny_class()

## Elliptic curves in class 16562.bv

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16562.bv1 16562bo6 [1, 1, 1, -22611443, 41375346865] [2] 622080
16562.bv2 16562bo5 [1, 1, 1, -1412083, 647136433] [2] 311040
16562.bv3 16562bo4 [1, 1, 1, -294148, 50208829] [2] 207360
16562.bv4 16562bo2 [1, 1, 1, -87123, -9927793] [2] 69120
16562.bv5 16562bo1 [1, 1, 1, -4313, -222461] [2] 34560 $$\Gamma_0(N)$$-optimal
16562.bv6 16562bo3 [1, 1, 1, 37092, 4630205] [2] 103680

## Rank

sage: E.rank()

The elliptic curves in class 16562.bv have rank $$1$$.

## Modular form 16562.2.a.bv

sage: E.q_eigenform(10)

$$q + q^{2} + 2q^{3} + q^{4} + 2q^{6} + q^{8} + q^{9} + 2q^{12} + q^{16} - 6q^{17} + q^{18} + 2q^{19} + O(q^{20})$$

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 2 & 3 & 9 & 18 & 6 \\ 2 & 1 & 6 & 18 & 9 & 3 \\ 3 & 6 & 1 & 3 & 6 & 2 \\ 9 & 18 & 3 & 1 & 2 & 6 \\ 18 & 9 & 6 & 2 & 1 & 3 \\ 6 & 3 & 2 & 6 & 3 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.