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

• Label: 2.83.o_ic
• 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:	$1 + 14 x + 210 x^{2} + 1162 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.584202214349$, $\pm0.669206851205$
Angle rank:	$2$ (numerical)
Number field:	4.0.1907600.1
Galois group:	$D_{4}$
Jacobians:	$60$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8276$	$49027024$	$325462216004$	$2252316386775296$	$15516750442211090116$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$98$	$7114$	$569198$	$47458830$	$3939220698$	$326939212378$	$27136046684390$	$2252292323498334$	$186940255001290994$	$15516041184748654314$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 60 curves (of which all are hyperelliptic):

• $y^2=67 x^6+65 x^5+53 x^4+60 x^3+35 x^2+6 x+77$
• $y^2=59 x^6+6 x^5+78 x^4+71 x^3+x^2+56 x+53$
• $y^2=45 x^6+14 x^5+75 x^4+22 x^3+5 x^2+21 x+78$
• $y^2=76 x^6+73 x^5+45 x^4+68 x^3+81 x^2+24 x+7$
• $y^2=32 x^6+42 x^5+27 x^4+59 x^3+32 x^2+66 x+46$
• $y^2=x^6+34 x^5+15 x^4+74 x^3+15 x^2+80 x+39$
• $y^2=48 x^6+56 x^5+35 x^4+82 x^3+80 x^2+80 x+12$
• $y^2=51 x^6+73 x^5+79 x^4+82 x^3+42 x^2+7 x+8$
• $y^2=14 x^5+25 x^4+77 x^3+74 x^2+80 x+34$
• $y^2=76 x^6+5 x^5+12 x^4+32 x^3+23 x^2+35 x+78$
• $y^2=10 x^6+57 x^5+43 x^4+10 x^3+77 x^2+2 x+65$
• $y^2=13 x^6+33 x^5+55 x^4+17 x^3+79 x^2+48 x+15$
• $y^2=30 x^6+71 x^5+43 x^4+70 x^3+59 x^2+49 x+51$
• $y^2=4 x^6+72 x^5+34 x^4+64 x^3+41 x^2+75 x+82$
• $y^2=69 x^6+39 x^5+50 x^4+69 x^3+12 x^2+76 x+3$
• $y^2=6 x^6+45 x^5+16 x^4+22 x^3+42 x^2+24 x+40$
• $y^2=22 x^6+35 x^5+51 x^4+82 x^3+10 x^2+x+34$
• $y^2=70 x^6+78 x^5+32 x^4+49 x^3+16 x^2+25 x+10$
• $y^2=5 x^6+37 x^5+76 x^4+62 x^3+26 x^2+81 x+72$
• $y^2=7 x^6+10 x^5+38 x^4+47 x^3+40 x^2+53 x+35$
• and

• $y^2=18 x^6+61 x^5+9 x^4+56 x^3+55 x^2+26 x+40$
• $y^2=42 x^6+26 x^5+76 x^4+8 x^3+9 x^2+74 x+7$
• $y^2=4 x^6+80 x^5+9 x^4+x^3+34 x^2+15 x+44$
• $y^2=63 x^6+43 x^5+78 x^4+56 x^3+4 x^2+34$
• $y^2=30 x^6+51 x^5+23 x^4+22 x^3+27 x^2+76 x+29$
• $y^2=53 x^6+64 x^5+79 x^4+12 x^3+77 x^2+3 x+9$
• $y^2=40 x^6+16 x^5+8 x^4+46 x^3+60 x^2+76 x+6$
• $y^2=82 x^6+74 x^5+52 x^4+23 x^3+45 x^2+52 x+22$
• $y^2=7 x^6+34 x^5+75 x^4+33 x^3+68 x^2+80 x+8$
• $y^2=21 x^6+30 x^5+19 x^4+48 x^3+30 x^2+30 x+63$
• $y^2=78 x^6+56 x^5+65 x^4+39 x^3+5 x^2+30 x+69$
• $y^2=54 x^6+60 x^5+20 x^4+69 x^3+61 x^2+36 x+58$
• $y^2=75 x^6+66 x^4+37 x^3+31 x^2+44 x+66$
• $y^2=11 x^6+16 x^5+20 x^4+17 x^3+31 x^2+47$
• $y^2=27 x^6+81 x^5+23 x^4+77 x^3+42 x^2+4 x$
• $y^2=53 x^6+43 x^5+12 x^4+45 x^3+3 x^2+33 x+3$
• $y^2=60 x^6+63 x^5+4 x^4+11 x^3+68 x^2+55 x+66$
• $y^2=57 x^6+28 x^5+11 x^4+2 x^3+43 x^2+54 x+80$
• $y^2=44 x^6+42 x^5+48 x^4+43 x^3+24 x^2+80 x+62$
• $y^2=37 x^6+40 x^4+71 x^3+5 x^2+42 x+81$
• $y^2=50 x^6+46 x^5+51 x^4+33 x^3+35 x^2+59 x+70$
• $y^2=64 x^6+73 x^5+10 x^4+45 x^3+28 x^2+55 x+46$
• $y^2=76 x^6+26 x^5+22 x^4+40 x^3+31 x^2+12 x+22$
• $y^2=31 x^6+42 x^5+43 x^4+44 x^3+72 x^2+42 x$
• $y^2=34 x^6+79 x^5+4 x^4+42 x^3+70 x^2+43 x+10$
• $y^2=40 x^6+77 x^5+32 x^4+28 x^3+81 x^2+76 x+56$
• $y^2=26 x^6+73 x^5+45 x^4+23 x^3+27 x^2+38 x+4$
• $y^2=75 x^6+49 x^5+80 x^4+42 x^3+47 x^2+34 x+38$
• $y^2=11 x^6+57 x^5+51 x^4+64 x^3+34 x^2+48 x+27$
• $y^2=51 x^6+17 x^5+39 x^4+61 x^3+37 x^2+69 x+28$
• $y^2=54 x^6+34 x^5+60 x^4+24 x^3+26 x^2+21 x+60$
• $y^2=5 x^6+15 x^5+69 x^4+42 x^3+11 x^2+44 x+65$
• $y^2=18 x^6+30 x^5+67 x^4+6 x^3+72 x^2+63 x+81$
• $y^2=32 x^6+11 x^5+6 x^4+31 x^3+62 x^2+22 x+43$
• $y^2=27 x^6+7 x^5+56 x^4+45 x^3+35 x^2+54 x+28$
• $y^2=19 x^6+70 x^5+79 x^4+24 x^3+46 x^2+3 x+77$
• $y^2=51 x^6+77 x^5+54 x^4+31 x^3+74 x^2+3 x+66$
• $y^2=67 x^6+32 x^5+41 x^4+44 x^3+27 x^2+50 x+69$
• $y^2=80 x^6+71 x^5+42 x^4+7 x^3+37 x^2+47 x+59$
• $y^2=39 x^6+57 x^5+57 x^4+44 x^3+35 x^2+16 x+7$

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 4.0.1907600.1.

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.ao_ic	$2$	(not in LMFDB)