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

• Label: 2.83.abd_oh
• 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:	$1 - 29 x + 371 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.126930498020$, $\pm0.266276878158$
Angle rank:	$2$ (numerical)
Number field:	4.0.4038237.1
Galois group:	$D_{4}$
Jacobians:	$12$
Isomorphism classes:	12

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4825$	$46788025$	$327322224475$	$2252948442866125$	$15516494014708546000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$55$	$6791$	$572455$	$47472147$	$3939155600$	$326940865499$	$27136051294505$	$2252292239859283$	$186940255770940645$	$15516041196283813286$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=69x^6+26x^5+67x^4+29x^3+76x^2+41x+13$
• $y^2=66x^6+5x^5+56x^4+18x^3+79x^2+23x+82$
• $y^2=17x^6+34x^5+79x^4+59x^3+61x^2+64x+73$
• $y^2=34x^6+12x^5+80x^4+19x^3+25x^2+37x+57$
• $y^2=56x^6+28x^5+67x^4+77x^3+23x^2+56x+82$
• $y^2=13x^6+13x^5+3x^4+68x^3+34x+47$
• $y^2=45x^6+48x^5+42x^4+66x^3+25x^2+62x+1$
• $y^2=75x^6+64x^5+43x^4+71x^3+80x^2+34x+74$
• $y^2=60x^6+57x^5+38x^4+61x^3+34x^2+56x+44$
• $y^2=2x^6+26x^5+48x^4+5x^3+62x^2+39x+37$
• $y^2=14x^6+82x^5+63x^4+30x^3+8x^2+46x+50$
• $y^2=46x^6+23x^5+66x^4+5x^3+15x^2+5x+61$

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 4.0.4038237.1.

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.bd_oh	$2$	(not in LMFDB)