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

• Label: 2.151.abp_bbf
• 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:	$1 - 41 x + 707 x^{2} - 6191 x^{3} + 22801 x^{4}$
Frobenius angles:	$\pm0.0376027983571$, $\pm0.264041825482$
Angle rank:	$2$ (numerical)
Number field:	4.0.10258797.1
Galois group:	$D_{4}$
Jacobians:	$16$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$17277$	$513835257$	$11852073122643$	$270283267133336925$	$6162664960037073959952$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$111$	$22535$	$3442419$	$519889891$	$78502560276$	$11853904559627$	$1789940517366441$	$270281036542453171$	$40812436746147736809$	$6162677950344140175230$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 16 curves (of which all are hyperelliptic):

• $y^2=81 x^6+88 x^5+126 x^4+109 x^3+115 x^2+66 x+54$
• $y^2=137 x^6+55 x^5+4 x^4+120 x^3+110 x^2+42 x+147$
• $y^2=104 x^6+43 x^5+144 x^4+17 x^3+56 x^2+17 x+89$
• $y^2=127 x^6+80 x^5+55 x^4+94 x^3+39 x+21$
• $y^2=116 x^6+127 x^5+109 x^4+32 x^3+49 x^2+30 x+107$
• $y^2=54 x^6+97 x^5+98 x^4+80 x^3+110 x^2+56 x+149$
• $y^2=13 x^6+84 x^5+43 x^4+56 x^3+144 x^2+77 x+11$
• $y^2=89 x^6+108 x^5+124 x^4+29 x^3+6 x^2+143 x+92$
• $y^2=115 x^6+32 x^5+121 x^4+119 x^3+131 x^2+116 x+103$
• $y^2=44 x^6+26 x^5+109 x^4+98 x^3+149 x^2+134 x+73$
• $y^2=131 x^6+98 x^5+79 x^4+102 x^3+47 x^2+130 x+52$
• $y^2=49 x^6+110 x^5+23 x^4+77 x^3+89 x^2+66 x+67$
• $y^2=64 x^6+138 x^5+140 x^4+72 x^3+65 x^2+23 x+53$
• $y^2=82 x^6+69 x^5+109 x^4+85 x^3+105 x^2+127 x+87$
• $y^2=123 x^6+138 x^5+51 x^4+49 x^3+15 x^2+24 x+148$
• $y^2=119 x^6+79 x^5+115 x^4+133 x^3+29 x^2+13 x+92$

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 4.0.10258797.1.

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.bp_bbf	$2$	(not in LMFDB)