# Properties

 Label 1.307.n Base Field $\F_{307}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

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## Invariants

 Base field: $\F_{307}$ Dimension: $1$ L-polynomial: $1 + 13 x + 307 x^{2}$ Frobenius angles: $\pm0.620976308961$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-1059})$$ Galois group: $C_2$ Jacobians: 6

This isogeny class is simple and geometrically simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $1$ Slopes: $[0, 1]$

## Point counts

This isogeny class contains the Jacobians of 6 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 321 94695 28924668 8882864475 2727045443391 837201954018960 257021010988832733 78905450535316732275 24223973308830311940036 7436759805832905048225975

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 321 94695 28924668 8882864475 2727045443391 837201954018960 257021010988832733 78905450535316732275 24223973308830311940036 7436759805832905048225975

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{307}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-1059})$$.
All geometric endomorphisms are defined over $\F_{307}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.307.an $2$ (not in LMFDB)