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

• Label: 2.83.abh_qv
• 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:	$1 - 33 x + 437 x^{2} - 2739 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.0821076990436$, $\pm0.180078914894$
Angle rank:	$2$ (numerical)
Number field:	4.0.51525.2
Galois group:	$D_{4}$
Jacobians:	$4$
Isomorphism classes:	4

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$4555$	$46000945$	$326431847605$	$2252373940644525$	$15516374481032902000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$51$	$6675$	$570897$	$47460043$	$3939125256$	$326941454175$	$27136060532667$	$2252292294643843$	$186940255537323621$	$15516041187486819750$

Jacobians and polarizations

This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=32x^6+60x^5+43x^4+81x^3+61x^2+18x+78$
• $y^2=34x^6+33x^5+42x^4+33x^3+25x^2+17x+22$
• $y^2=58x^6+41x^5+10x^4+6x^3+42x^2+42x+73$
• $y^2=8x^6+82x^5+65x^4+51x^3+61x^2+40x+22$

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 4.0.51525.2.

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.bh_qv	$2$	(not in LMFDB)