Properties

 Label 2.16.ah_bk Base Field $\F_{2^{4}}$ Dimension $2$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{2^{4}}$ Dimension: $2$ L-polynomial: $1 - 7 x + 36 x^{2} - 112 x^{3} + 256 x^{4}$ Frobenius angles: $\pm0.206663904003$, $\pm0.474998167614$ Angle rank: $2$ (numerical) Number field: 4.0.101277.1 Galois group: $D_{4}$ Jacobians: 8

This isogeny class is simple and geometrically simple.

Newton polygon

 $p$-rank: $1$ Slopes: $[0, 1/2, 1/2, 1]$

Point counts

This isogeny class contains the Jacobians of 8 curves, and hence is principally polarizable:

• $y^2+xy=ax^5+(a^3+a^2)x^3+(a^3+a^2)x^2+x$
• $y^2+xy=a^2x^5+(a^3+a^2+a+1)x^3+(a^3+1)x^2+x$
• $y^2+xy=(a+1)x^5+(a^3+a)x^3+(a^3+1)x^2+x$
• $y^2+xy=(a^3+a+1)x^5+a^3x^3+(a^3+1)x^2+x$
• $y^2+xy=(a^2+1)x^5+a^3x^3+(a^3+a+1)x^2+x$
• $y^2+xy=(a^3+a^2+a)x^5+(a^3+a)x^3+(a^3+1)x^2+x$
• $y^2+xy=(a^3+a^2+1)x^5+(a^3+a^2+a+1)x^3+(a^3+a^2)x^2+x$
• $y^2+xy=(a^3+1)x^5+(a^3+a^2)x^3+(a^3+a^2+1)x^2+x$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 174 71688 17102286 4291673808 1100825995494 281697704301528 72063658356938814 18446027890056000672 4722310484285499085014 1208925194500744065536808

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 10 280 4174 65488 1049830 16790488 268458046 4294800544 68718661846 1099511059240

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{2^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.101277.1.
All geometric endomorphisms are defined over $\F_{2^{4}}$.

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 2.16.h_bk $2$ 2.256.x_jg