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

• Label: 2.83.q_iw
• Base field: $\F_{83}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{83}$
Dimension:	$2$
L-polynomial:	$( 1 + 8 x + 83 x^{2} )^{2}$
	$1 + 16 x + 230 x^{2} + 1328 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.644687400264$, $\pm0.644687400264$
Angle rank:	$1$ (numerical)
Jacobians:	$46$
Cyclic group of points:	no
Non-cyclic primes:	$2, 23$

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8464$	$48888064$	$325251214864$	$2252612587196416$	$15516796302606066064$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$100$	$7094$	$568828$	$47465070$	$3939232340$	$326938279718$	$27136051828076$	$2252292399204574$	$186940253861424964$	$15516041184588337814$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 46 curves (of which all are hyperelliptic):

• $y^2=77 x^6+46 x^4+46 x^2+77$
• $y^2=73 x^6+13 x^5+50 x^4+29 x^3+8 x^2+42 x+63$
• $y^2=24 x^6+35 x^5+31 x^4+65 x^3+68 x^2+10 x+71$
• $y^2=20 x^5+39 x^4+79 x^3+14 x^2+22 x+33$
• $y^2=45 x^6+53 x^5+14 x^4+63 x^3+20 x^2+47 x+41$
• $y^2=40 x^6+20 x^5+64 x^4+56 x^3+61 x^2+72 x+6$
• $y^2=46 x^6+57 x^5+76 x^4+14 x^3+48 x^2+70 x+48$
• $y^2=66 x^6+46 x^5+49 x^4+53 x^3+14 x^2+23 x+35$
• $y^2=29 x^6+82 x^5+66 x^4+25 x^3+55 x^2+2 x+23$
• $y^2=2 x^6+80 x^5+47 x^4+29 x^3+81 x^2+43 x+3$
• $y^2=38 x^6+80 x^5+42 x^4+5 x^3+2 x^2+35 x+25$
• $y^2=47 x^5+63 x^4+37 x^3+22 x^2+46 x+73$
• $y^2=36 x^6+62 x^5+33 x^4+10 x^3+62 x^2+74 x+48$
• $y^2=63 x^6+78 x^5+73 x^4+52 x^3+22 x^2+58 x+50$
• $y^2=53 x^6+75 x^4+75 x^2+53$
• $y^2=8 x^6+51 x^5+62 x^4+78 x^3+13 x^2+56 x+29$
• $y^2=2 x^6+70 x^5+29 x^4+81 x^3+28 x^2+58 x+5$
• $y^2=69 x^6+11 x^5+75 x^4+45 x^3+68 x^2+57 x+50$
• $y^2=7 x^6+76 x^5+50 x^4+5 x^3+21 x^2+47 x+38$
• $y^2=78 x^6+28 x^5+41 x^4+11 x^3+5 x^2+71 x+18$
• and

• $y^2=29 x^6+67 x^5+14 x^4+33 x^3+14 x^2+67 x+29$
• $y^2=12 x^6+82 x^5+7 x^4+74 x^3+9 x^2+4 x+13$
• $y^2=76 x^6+79 x^5+43 x^4+47 x^3+24 x^2+66 x+61$
• $y^2=64 x^6+53 x^5+79 x^4+2 x^3+68 x^2+12 x+52$
• $y^2=61 x^6+51 x^5+26 x^4+24 x^3+25 x^2+73 x+76$
• $y^2=59 x^6+32 x^5+34 x^4+59 x^3+22 x^2+47 x+37$
• $y^2=58 x^6+60 x^5+17 x^4+3 x^3+25 x^2+56 x+63$
• $y^2=34 x^6+6 x^5+33 x^4+82 x^3+10 x^2+64 x+42$
• $y^2=61 x^6+8 x^5+23 x^4+68 x^3+72 x^2+21 x+10$
• $y^2=10 x^6+39 x^5+52 x^4+59 x^3+67 x^2+42 x+7$
• $y^2=6 x^6+61 x^4+61 x^2+6$
• $y^2=47 x^6+75 x^5+6 x^4+x^3+57 x^2+19 x+48$
• $y^2=33 x^6+79 x^5+26 x^4+75 x^3+17 x^2+9 x+25$
• $y^2=79 x^6+48 x^5+53 x^4+73 x^3+53 x^2+48 x+79$
• $y^2=4 x^6+16 x^5+37 x^4+12 x^3+40 x^2+24 x+24$
• $y^2=67 x^6+41 x^5+53 x^4+28 x^3+20 x^2+29 x+22$
• $y^2=21 x^6+64 x^5+26 x^4+81 x^3+73 x^2+30 x+8$
• $y^2=53 x^6+50 x^5+48 x^4+13 x^3+62 x^2+71 x+1$
• $y^2=37 x^6+51 x^5+41 x^4+66 x^3+58 x^2+55 x+21$
• $y^2=80 x^6+23 x^5+29 x^4+19 x^3+40 x^2+71 x+8$
• $y^2=52 x^6+24 x^5+48 x^4+x^3+66 x^2+49 x+69$
• $y^2=25 x^6+64 x^5+13 x^4+68 x^3+13 x^2+64 x+25$
• $y^2=51 x^6+56 x^5+57 x^4+41 x^3+25 x^2+56 x+67$
• $y^2=69 x^6+27 x^5+6 x^4+11 x^3+62 x^2+34 x+40$
• $y^2=40 x^6+57 x^5+16 x^4+8 x^3+78 x^2+30 x+20$
• $y^2=22 x^6+57 x^5+79 x^4+49 x^3+79 x^2+57 x+22$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{83}$

The isogeny class factors as 1.83.i^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-67}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.83.aq_iw	$2$	(not in LMFDB)
2.83.a_dy	$2$	(not in LMFDB)
2.83.ai_at	$3$	(not in LMFDB)