Abelian variety isogeny class 2.151.abt_bfb over $\F_{151}$

• Label: 2.151.abt_bfb
• Base field: $\F_{151}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{151}$
Dimension:	$2$
L-polynomial:	$1 - 45 x + 807 x^{2} - 6795 x^{3} + 22801 x^{4}$
Frobenius angles:	$\pm0.0891857960344$, $\pm0.164105848651$
Angle rank:	$2$ (numerical)
Number field:	4.0.169525.1
Galois group:	$D_{4}$
Jacobians:	$11$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

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

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$16769$	$510599281$	$11845087524119$	$270281912667724525$	$6162707695131643360304$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$107$	$22391$	$3440387$	$519887283$	$78503104652$	$11853919224371$	$1789940757601817$	$270281039350098163$	$40812436768520550197$	$6162677950417428131006$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 11 curves (of which all are hyperelliptic):

• $y^2=3 x^6+25 x^5+29 x^4+89 x^3+28 x^2+86 x+79$
• $y^2=133 x^6+141 x^5+141 x^4+66 x^3+103 x^2+87 x+48$
• $y^2=12 x^6+102 x^5+3 x^4+3 x^3+38 x^2+53 x+141$
• $y^2=87 x^6+23 x^5+105 x^4+148 x^3+31 x^2+24 x+70$
• $y^2=14 x^6+94 x^5+105 x^4+85 x^3+11 x^2+136 x+91$
• $y^2=30 x^6+136 x^5+4 x^4+66 x^3+9 x^2+144 x+86$
• $y^2=30 x^6+77 x^5+50 x^4+142 x^3+44 x^2+4 x+74$
• $y^2=101 x^6+33 x^5+116 x^4+69 x^3+44 x^2+4 x+30$
• $y^2=35 x^6+12 x^5+38 x^4+45 x^3+39 x^2+110 x+135$
• $y^2=81 x^6+16 x^5+17 x^4+30 x^3+66 x^2+66 x+21$
• $y^2=57 x^6+10 x^5+39 x^4+135 x^3+105 x^2+137 x+85$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{151}$.

Endomorphism algebra over $\F_{151}$

The endomorphism algebra of this simple isogeny class is 4.0.169525.1.

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
2.151.bt_bfb	$2$	(not in LMFDB)