Abelian variety isogeny class 2.163.abt_bft over $\F_{163}$

• Label: 2.163.abt_bft
• Base field: $\F_{163}$
• 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:	$\F_{163}$
Dimension:	$2$
L-polynomial:	$1 - 45 x + 825 x^{2} - 7335 x^{3} + 26569 x^{4}$
Frobenius angles:	$\pm0.0521334521506$, $\pm0.217387748284$
Angle rank:	$2$ (numerical)
Number field:	4.0.3785341.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$20015$	$696021625$	$18747770750345$	$498316073399828125$	$13239657817526454753200$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$119$	$26195$	$4328993$	$705918363$	$115063806944$	$18755369768135$	$3057125188150523$	$498311412990880003$	$81224760514255585769$	$13239635966836934121350$

Jacobians and polarizations

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

• $y^2=2x^6+18x^5+141x^4+87x^3+98x^2+121x+50$
• $y^2=89x^6+91x^5+144x^4+144x^3+10x^2+53x+117$
• $y^2=99x^6+43x^5+159x^4+69x^3+116x^2+2x+2$
• $y^2=18x^6+88x^5+126x^4+152x^3+66x^2+5x+139$
• $y^2=150x^6+7x^5+96x^4+146x^3+72x^2+87x+11$
• $y^2=154x^6+78x^5+155x^4+3x^3+132x^2+157x+72$
• $y^2=154x^6+46x^5+15x^4+134x^3+126x^2+141x+14$
• $y^2=103x^6+56x^5+62x^4+30x^3+148x^2+158x+60$
• $y^2=101x^6+61x^5+143x^4+119x^3+59x^2+11x+78$
• $y^2=134x^6+50x^5+121x^4+26x^3+44x^2+40x+150$
• $y^2=143x^6+159x^5+61x^4+53x^3+53x^2+64x+63$
• $y^2=109x^6+13x^5+16x^4+95x^3+161x^2+59x+120$
• $y^2=144x^6+116x^5+107x^4+42x^3+141x^2+59x$
• $y^2=69x^6+135x^5+124x^4+31x^3+68x^2+142x+79$
• $y^2=76x^6+111x^5+154x^4+111x^3+47x^2+99x+91$
• $y^2=26x^6+39x^5+123x^4+135x^3+145x^2+105x+42$
• $y^2=30x^6+139x^5+160x^4+110x^3+24x^2+51x+128$
• $y^2=31x^6+20x^5+156x^4+63x^3+46x^2+59x+130$
• $y^2=70x^6+125x^5+130x^4+20x^3+126x^2+115x+26$
• $y^2=31x^6+78x^5+95x^4+157x^3+118x^2+111x+111$
• $y^2=141x^6+123x^5+12x^4+159x^3+146x^2+9x+107$
• $y^2=61x^6+157x^5+4x^4+3x^3+69x^2+146x+161$
• $y^2=131x^6+66x^5+101x^4+87x^3+80x^2+13x+11$
• $y^2=112x^6+57x^5+61x^4+154x^3+111x^2+135x+56$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{163}$.

Endomorphism algebra over $\F_{163}$

The endomorphism algebra of this simple isogeny class is 4.0.3785341.1.

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
2.163.bt_bft	$2$	(not in LMFDB)