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

• Label: 2.179.abu_bhr
• Base field: $\F_{179}$
• 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:	$\F_{179}$
Dimension:	$2$
L-polynomial:	$1 - 46 x + 875 x^{2} - 8234 x^{3} + 32041 x^{4}$
Frobenius angles:	$\pm0.0472350362762$, $\pm0.239477740183$
Angle rank:	$2$ (numerical)
Number field:	4.0.753552.2
Galois group:	$D_{4}$
Jacobians:	$24$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$24637$	$1014970489$	$32886724678288$	$1053970966527948937$	$33769953695883889181797$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$134$	$31676$	$5734052$	$1026636084$	$183766062634$	$32894108488550$	$5888046148049374$	$1053960286138294180$	$188658891680411062556$	$33769941616132099339436$

Jacobians and polarizations

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

• $y^2=110x^6+119x^5+133x^4+47x^3+97x^2+77x+70$
• $y^2=153x^6+98x^5+101x^4+97x^3+63x^2+162x+165$
• $y^2=160x^6+129x^5+23x^4+40x^3+124x^2+151x+123$
• $y^2=40x^6+18x^5+31x^4+47x^3+83x^2+8x+140$
• $y^2=98x^6+119x^5+31x^4+148x^3+76x^2+50x+55$
• $y^2=130x^6+102x^5+33x^4+16x^3+121x^2+75x+29$
• $y^2=121x^6+108x^5+20x^4+155x^3+144x^2+98x+104$
• $y^2=147x^6+110x^5+149x^4+37x^3+130x^2+51x+15$
• $y^2=43x^6+40x^5+39x^4+19x^3+166x^2+114x+165$
• $y^2=178x^6+137x^5+80x^4+136x^3+110x^2+39x+157$
• $y^2=38x^6+114x^5+64x^4+40x^3+3x^2+37x+2$
• $y^2=90x^6+29x^5+49x^4+17x^3+167x^2+150x+113$
• $y^2=99x^6+160x^5+169x^4+144x^3+160x^2+175x+58$
• $y^2=122x^6+61x^5+124x^4+114x^3+73x^2+48x+33$
• $y^2=111x^6+39x^5+22x^4+158x^3+154x^2+104x+92$
• $y^2=155x^6+77x^5+157x^4+73x^3+60x^2+104x+89$
• $y^2=65x^6+90x^5+124x^4+8x^3+106x^2+127x+168$
• $y^2=142x^6+138x^5+49x^4+66x^3+37x^2+116x+114$
• $y^2=154x^6+94x^5+20x^4+80x^3+32x^2+79x+147$
• $y^2=133x^6+23x^5+120x^4+131x^3+6x^2+143x+50$
• $y^2=78x^6+45x^5+41x^4+125x^3+163x^2+35x+31$
• $y^2=165x^6+136x^5+66x^4+31x^3+163x^2+x+55$
• $y^2=43x^6+118x^5+110x^4+165x^3+55x^2+171x+55$
• $y^2=33x^6+11x^5+24x^4+119x^3+103x^2+172x+82$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{179}$

The endomorphism algebra of this simple isogeny class is 4.0.753552.2.

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.bu_bhr	$2$	(not in LMFDB)