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

• Label: 2.83.abe_ov
• 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:	$1 - 30 x + 385 x^{2} - 2490 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.0929518943327$, $\pm0.258138369806$
Angle rank:	$2$ (numerical)
Number field:	4.0.2765376.2
Galois group:	$D_{4}$
Jacobians:	$28$
Isomorphism classes:	28

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4755$	$46575225$	$327043327140$	$2252686441865625$	$15516288762724438275$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$54$	$6760$	$571968$	$47466628$	$3939103494$	$326940404830$	$27136047178098$	$2252292204957508$	$186940255564895184$	$15516041196883949800$

Jacobians and polarizations

This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=43x^6+80x^5+33x^4+9x^3+19x^2+39x+9$
• $y^2=22x^6+73x^5+9x^4+31x^3+23x^2+70x+52$
• $y^2=8x^6+31x^5+14x^4+7x^3+7x^2+10x+67$
• $y^2=35x^6+15x^5+42x^4+37x^3+54x^2+69x+40$
• $y^2=10x^6+27x^5+52x^4+28x^3+77x^2+69x+43$
• $y^2=73x^6+40x^5+2x^4+43x^3+10x^2+2x+53$
• $y^2=25x^6+61x^5+82x^4+50x^3+56x^2+65x+3$
• $y^2=62x^6+73x^5+55x^4+x^3+75x^2+63x+57$
• $y^2=81x^6+54x^5+74x^4+66x^3+5x^2+66x+72$
• $y^2=82x^6+46x^5+48x^4+53x^3+63x^2+48x+12$
• $y^2=32x^6+61x^5+14x^4+72x^3+58x^2+24x+43$
• $y^2=30x^6+37x^5+22x^4+74x^3+69x^2+45x+73$
• $y^2=6x^6+5x^5+66x^4+64x^2+34x+49$
• $y^2=35x^6+72x^5+74x^4+35x^3+20x^2+9x+54$
• $y^2=43x^6+54x^5+14x^4+77x^3+40x^2+16x+34$
• $y^2=19x^6+6x^5+36x^4+7x^3+39x^2+63x+62$
• $y^2=14x^6+45x^5+16x^4+81x^3+6x^2+21x+43$
• $y^2=x^6+70x^5+22x^4+54x^3+66x^2+77x+51$
• $y^2=32x^6+71x^5+60x^4+35x^3+61x^2+33x+57$
• $y^2=42x^6+59x^5+59x^4+30x^3+26x^2+30x+76$
• $y^2=20x^6+44x^5+77x^4+4x^3+15x^2+81x+5$
• $y^2=63x^6+16x^5+31x^4+32x^3+81x^2+26x+78$
• $y^2=13x^6+3x^5+16x^4+16x^3+12x^2+31x+46$
• $y^2=19x^6+71x^5+70x^4+13x^3+6x^2+43x+26$
• $y^2=18x^6+26x^5+35x^4+52x^3+8x^2+21x+26$
• $y^2=30x^6+11x^5+25x^4+62x^3+76x^2+54x+33$
• $y^2=80x^6+74x^5+82x^4+63x^3+71x^2+18x+53$
• $y^2=2x^6+24x^5+75x^4+57x^3+52x^2+18x+79$

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 4.0.2765376.2.

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
2.83.be_ov	$2$	(not in LMFDB)