# Properties

 Base field $$\Q(\sqrt{13})$$ Label 2.2.13.1-81.1-a Conductor 81.1 Rank $$0$$

# Related objects

## Base field $$\Q(\sqrt{13})$$

Generator $$a$$, with minimal polynomial $$x^{2} - x - 3$$; class number $$1$$.

## Elliptic curves in class 81.1-a over $$\Q(\sqrt{13})$$

Isogeny class 81.1-a contains 12 curves linked by isogenies of degrees dividing 24.

## Rank

Rank: $$0$$

## Isogeny matrix

$$\left(\begin{array}{rrrrrrrrrrrr} 1 & 24 & 8 & 3 & 6 & 4 & 8 & 12 & 12 & 2 & 24 & 4 \\ 24 & 1 & 3 & 8 & 4 & 6 & 12 & 8 & 2 & 12 & 4 & 24 \\ 8 & 3 & 1 & 24 & 12 & 2 & 4 & 24 & 6 & 4 & 12 & 8 \\ 3 & 8 & 24 & 1 & 2 & 12 & 24 & 4 & 4 & 6 & 8 & 12 \\ 6 & 4 & 12 & 2 & 1 & 6 & 12 & 2 & 2 & 3 & 4 & 6 \\ 4 & 6 & 2 & 12 & 6 & 1 & 2 & 12 & 3 & 2 & 6 & 4 \\ 8 & 12 & 4 & 24 & 12 & 2 & 1 & 24 & 6 & 4 & 3 & 8 \\ 12 & 8 & 24 & 4 & 2 & 12 & 24 & 1 & 4 & 6 & 8 & 3 \\ 12 & 2 & 6 & 4 & 2 & 3 & 6 & 4 & 1 & 6 & 2 & 12 \\ 2 & 12 & 4 & 6 & 3 & 2 & 4 & 6 & 6 & 1 & 12 & 2 \\ 24 & 4 & 12 & 8 & 4 & 6 & 3 & 8 & 2 & 12 & 1 & 24 \\ 4 & 24 & 8 & 12 & 6 & 4 & 8 & 3 & 12 & 2 & 24 & 1 \end{array}\right)$$