Abelian variety isogeny class 2.83.abe_ow over $\F_{83}$

• Label: 2.83.abe_ow
• Base field: $\F_{83}$
• 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:	$\F_{83}$
Dimension:	$2$
L-polynomial:	$1 - 30 x + 386 x^{2} - 2490 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.105130850416$, $\pm0.252955120358$
Angle rank:	$2$ (numerical)
Number field:	4.0.147600.1
Galois group:	$D_{4}$
Jacobians:	$24$
Isomorphism classes:	32

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4756$	$46589776$	$327094989124$	$2252784138230016$	$15516414026135264836$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$54$	$6762$	$572058$	$47468686$	$3939135294$	$326940766458$	$27136050193698$	$2252292220810078$	$186940255561645734$	$15516041195712144522$

Jacobians and polarizations

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

• $y^2=68x^6+26x^5+5x^4+26x^3+8x^2+9x+82$
• $y^2=54x^6+14x^5+19x^4+10x^3+32x^2+65x+74$
• $y^2=8x^6+69x^5+17x^4+59x^3+79x^2+13x+72$
• $y^2=33x^6+23x^5+3x^4+29x^3+53x^2+4x+20$
• $y^2=55x^6+49x^5+58x^4+68x^3+78x^2+80x+8$
• $y^2=3x^6+15x^5+77x^4+7x^3+15x^2+74x+75$
• $y^2=2x^6+65x^5+56x^4+9x^3+67x^2+74x+9$
• $y^2=70x^6+4x^5+27x^4+32x^3+74x^2+57x+76$
• $y^2=34x^6+82x^5+68x^4+39x^3+48x^2+76x+66$
• $y^2=47x^6+26x^5+78x^4+23x^3+18x^2+78x+41$
• $y^2=6x^6+64x^5+71x^4+81x^3+21x^2+69x+31$
• $y^2=81x^5+36x^4+x^3+38x^2+77x+34$
• $y^2=76x^6+82x^5+13x^4+27x^3+65x^2+31x+60$
• $y^2=18x^6+69x^5+72x^4+42x^3+41x^2+3$
• $y^2=38x^6+64x^5+49x^4+42x^3+9x^2+49x+12$
• $y^2=53x^6+68x^5+26x^4+3x^3+65x^2+49x+78$
• $y^2=56x^6+64x^5+70x^4+27x^3+2x^2+52x+24$
• $y^2=55x^6+46x^5+54x^4+15x^3+17x^2+81x+24$
• $y^2=79x^6+64x^5+41x^4+81x^3+4x^2+16x+45$
• $y^2=52x^6+25x^5+74x^4+14x^3+23x^2+30x+58$
• $y^2=5x^6+44x^5+9x^4+33x^3+77x^2+12x+19$
• $y^2=58x^6+28x^5+7x^4+38x^3+56x^2+6x+39$
• $y^2=32x^6+42x^5+19x^4+37x^3+63x^2+44$
• $y^2=53x^6+45x^5+57x^4+11x^3+22x^2+5x+67$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{83}$.

Endomorphism algebra over $\F_{83}$

The endomorphism algebra of this simple isogeny class is 4.0.147600.1.

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
2.83.be_ow	$2$	(not in LMFDB)