Abelian variety isogeny class 2.179.abu_bic over $\F_{179}$

• Label: 2.179.abu_bic
• Base field: $\F_{179}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{179}$
Dimension:	$2$
L-polynomial:	$( 1 - 24 x + 179 x^{2} )( 1 - 22 x + 179 x^{2} )$
	$1 - 46 x + 886 x^{2} - 8234 x^{3} + 32041 x^{4}$
Frobenius angles:	$\pm0.145797798478$, $\pm0.192758452317$
Angle rank:	$2$ (numerical)
Jacobians:	$24$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24648$	$1015694784$	$32895442952424$	$1054026780125829120$	$33770201968343204326248$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$134$	$31698$	$5735570$	$1026690446$	$183767413654$	$32894134150626$	$5888046529756546$	$1053960290397230686$	$188658891707887595750$	$33769941615973595014578$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which all are hyperelliptic):

• $y^2=21 x^6+105 x^5+155 x^4+39 x^3+155 x^2+105 x+21$
• $y^2=96 x^6+45 x^5+8 x^4+62 x^3+98 x^2+141 x+69$
• $y^2=34 x^6+161 x^5+63 x^4+159 x^3+92 x^2+57 x+143$
• $y^2=178 x^6+83 x^5+151 x^4+77 x^3+151 x^2+83 x+178$
• $y^2=93 x^6+16 x^5+77 x^4+141 x^3+77 x^2+16 x+93$
• $y^2=53 x^6+144 x^5+178 x^4+166 x^3+178 x^2+144 x+53$
• $y^2=154 x^6+129 x^5+115 x^4+33 x^3+162 x^2+117 x+140$
• $y^2=x^6+88 x^5+147 x^4+64 x^3+147 x^2+88 x+1$
• $y^2=69 x^6+119 x^5+122 x^4+34 x^3+55 x^2+40 x+170$
• $y^2=105 x^6+42 x^5+72 x^4+100 x^3+44 x^2+19 x+34$
• $y^2=159 x^6+66 x^5+79 x^4+138 x^3+79 x^2+66 x+159$
• $y^2=159 x^6+132 x^5+34 x^4+63 x^3+34 x^2+132 x+159$
• $y^2=148 x^6+40 x^5+116 x^4+92 x^3+116 x^2+40 x+148$
• $y^2=34 x^6+102 x^5+36 x^4+68 x^3+169 x^2+104 x+176$
• $y^2=51 x^6+126 x^5+123 x^4+7 x^3+92 x^2+46 x+65$
• $y^2=26 x^6+96 x^5+164 x^4+78 x^3+136 x^2+92 x+148$
• $y^2=75 x^6+103 x^5+111 x^4+116 x^3+109 x^2+122 x+25$
• $y^2=62 x^6+40 x^5+135 x^4+73 x^3+13 x^2+164 x+134$
• $y^2=170 x^6+154 x^5+88 x^4+14 x^3+88 x^2+154 x+170$
• $y^2=93 x^6+146 x^5+172 x^4+54 x^3+172 x^2+146 x+93$
• $y^2=26 x^6+165 x^5+60 x^4+110 x^3+60 x^2+165 x+26$
• $y^2=33 x^6+170 x^5+138 x^4+12 x^3+138 x^2+170 x+33$
• $y^2=170 x^6+39 x^5+35 x^4+178 x^3+122 x^2+135 x+35$
• $y^2=38 x^6+2 x^5+64 x^4+135 x^3+64 x^2+2 x+38$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{179}$.

Endomorphism algebra over $\F_{179}$

The isogeny class factors as 1.179.ay $\times$ 1.179.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.179.ay : \(\Q(\sqrt{-35}) \).
• 1.179.aw : \(\Q(\sqrt{-58}) \).

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
2.179.ac_ago	$2$	(not in LMFDB)
2.179.c_ago	$2$	(not in LMFDB)
2.179.bu_bic	$2$	(not in LMFDB)