# Properties

 Base field $$\Q(\zeta_{16})^+$$ Label 4.4.2048.1-1.1-a Conductor 1.1 Rank $$0$$

# Related objects

## Base field $$\Q(\zeta_{16})^+$$

Generator $$a$$, with minimal polynomial $$x^{4} - 4 x^{2} + 2$$; class number $$1$$.

## Elliptic curves in class 1.1-a over $$\Q(\zeta_{16})^+$$

Isogeny class 1.1-a contains 12 curves linked by isogenies of degrees dividing 40.

## Rank

Rank: $$0$$

## Isogeny matrix

$$\left(\begin{array}{rrrrrrrrrrrr} 1 & 10 & 2 & 20 & 4 & 8 & 8 & 4 & 40 & 5 & 20 & 40 \\ 10 & 1 & 5 & 2 & 10 & 20 & 20 & 10 & 4 & 2 & 2 & 4 \\ 2 & 5 & 1 & 10 & 2 & 4 & 4 & 2 & 20 & 10 & 10 & 20 \\ 20 & 2 & 10 & 1 & 5 & 10 & 10 & 20 & 2 & 4 & 4 & 2 \\ 4 & 10 & 2 & 5 & 1 & 2 & 2 & 4 & 10 & 20 & 20 & 10 \\ 8 & 20 & 4 & 10 & 2 & 1 & 4 & 8 & 20 & 40 & 40 & 5 \\ 8 & 20 & 4 & 10 & 2 & 4 & 1 & 8 & 5 & 40 & 40 & 20 \\ 4 & 10 & 2 & 20 & 4 & 8 & 8 & 1 & 40 & 20 & 5 & 40 \\ 40 & 4 & 20 & 2 & 10 & 20 & 5 & 40 & 1 & 8 & 8 & 4 \\ 5 & 2 & 10 & 4 & 20 & 40 & 40 & 20 & 8 & 1 & 4 & 8 \\ 20 & 2 & 10 & 4 & 20 & 40 & 40 & 5 & 8 & 4 & 1 & 8 \\ 40 & 4 & 20 & 2 & 10 & 5 & 20 & 40 & 4 & 8 & 8 & 1 \end{array}\right)$$