# Properties

 Label 1.421.abe Base Field $\F_{421}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{421}$ Dimension: $1$ L-polynomial: $1 - 30 x + 421 x^{2}$ Frobenius angles: $\pm0.239028144384$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-1})$$ Galois group: $C_2$ Jacobians: 14

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 14 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 392 177184 74629352 31414723200 13225456594952 5567914752653344 2344092096380466152 986862773183057164800 415469227534372348754312 174912544792444420431471904

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 392 177184 74629352 31414723200 13225456594952 5567914752653344 2344092096380466152 986862773183057164800 415469227534372348754312 174912544792444420431471904

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{421}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-1})$$.
All geometric endomorphisms are defined over $\F_{421}$.

## 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 1.421.be $2$ (not in LMFDB) 1.421.abc $4$ (not in LMFDB) 1.421.bc $4$ (not in LMFDB)