# Properties

 Label 16650.cb Number of curves $6$ Conductor $16650$ CM no Rank $1$ Graph

# Related objects

Show commands for: SageMath
sage: E = EllipticCurve("16650.cb1")

sage: E.isogeny_class()

## Elliptic curves in class 16650.cb

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
16650.cb1 16650bu3 [1, -1, 1, -76726130, -258660935503] [2] 1327104
16650.cb2 16650bu5 [1, -1, 1, -68203130, 215872164497] [2] 2654208
16650.cb3 16650bu4 [1, -1, 1, -6598130, -731015503] [2, 2] 1327104
16650.cb4 16650bu2 [1, -1, 1, -4798130, -4035815503] [2, 2] 663552
16650.cb5 16650bu1 [1, -1, 1, -190130, -109799503] [2] 331776 $$\Gamma_0(N)$$-optimal
16650.cb6 16650bu6 [1, -1, 1, 26206870, -5848595503] [2] 2654208

## Rank

sage: E.rank()

The elliptic curves in class 16650.cb have rank $$1$$.

## Modular form 16650.2.a.cb

sage: E.q_eigenform(10)

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

## 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.

$$\left(\begin{array}{rrrrrr} 1 & 8 & 4 & 2 & 4 & 8 \\ 8 & 1 & 2 & 4 & 8 & 4 \\ 4 & 2 & 1 & 2 & 4 & 2 \\ 2 & 4 & 2 & 1 & 2 & 4 \\ 4 & 8 & 4 & 2 & 1 & 8 \\ 8 & 4 & 2 & 4 & 8 & 1 \end{array}\right)$$

## Isogeny graph

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

The vertices are labelled with LMFDB labels.