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

• Label: 2.151.abt_bez
• 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:	$1 - 45 x + 805 x^{2} - 6795 x^{3} + 22801 x^{4}$
Frobenius angles:	$\pm0.0475440466108$, $\pm0.181284900557$
Angle rank:	$2$ (numerical)
Number field:	4.0.4901.1
Galois group:	$D_{4}$
Jacobians:	$15$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$16767$	$510504849$	$11844156000717$	$270276842053038141$	$6162687770964163730352$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$107$	$22387$	$3440117$	$519877531$	$78502850852$	$11853913913647$	$1789940663577467$	$270281037907191523$	$40812436749195383897$	$6162677950193975786302$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 15 curves (of which all are hyperelliptic):

• $y^2=133 x^6+24 x^5+76 x^4+139 x^3+97 x^2+34 x+71$
• $y^2=67 x^6+81 x^5+58 x^4+142 x^3+65 x^2+137 x+117$
• $y^2=60 x^6+43 x^5+127 x^4+139 x^3+117 x^2+33 x+142$
• $y^2=75 x^6+93 x^5+103 x^4+25 x^3+11 x^2+66 x+42$
• $y^2=34 x^6+41 x^5+130 x^4+41 x^3+32 x^2+17 x+26$
• $y^2=138 x^6+134 x^5+80 x^4+68 x^3+48 x^2+89 x+135$
• $y^2=37 x^6+31 x^4+148 x^3+148 x^2+3 x+70$
• $y^2=6 x^6+107 x^5+128 x^4+8 x^3+97 x^2+121 x+65$
• $y^2=21 x^6+33 x^5+18 x^4+45 x^3+105 x^2+89 x+7$
• $y^2=109 x^6+75 x^5+134 x^4+72 x^3+108 x^2+52 x+117$
• $y^2=150 x^6+78 x^5+134 x^4+76 x^3+34 x^2+24 x+58$
• $y^2=41 x^6+49 x^5+112 x^4+32 x^3+24 x^2+134 x+77$
• $y^2=44 x^6+112 x^5+91 x^4+45 x^3+96 x^2+145 x+141$
• $y^2=119 x^6+65 x^5+38 x^4+97 x^3+110 x^2+86 x+114$
• $y^2=126 x^6+61 x^5+115 x^4+44 x^3+86 x^2+89 x+15$

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 4.0.4901.1.

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_bez	$2$	(not in LMFDB)