Properties

 Label 1.421.c 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: $1 + 2 x + 421 x^{2}$ Frobenius angles: $\pm0.515519622707$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-105})$$ Galois group: $C_2$ Jacobians: 24

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 24 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 424 178080 74615944 31414024320 13225452401704 5567914864905120 2344092096940685704 986862773185402606080 415469227536066368824744 174912544792476727109412000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 424 178080 74615944 31414024320 13225452401704 5567914864905120 2344092096940685704 986862773185402606080 415469227536066368824744 174912544792476727109412000

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{421}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-105})$$.
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.ac $2$ (not in LMFDB)