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

• Label: 2.83.c_gl
• 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:	$( 1 + x + 83 x^{2} )^{2}$
	$1 + 2 x + 167 x^{2} + 166 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.517478306302$, $\pm0.517478306302$
Angle rank:	$1$ (numerical)
Jacobians:	$45$
Cyclic group of points:	no
Non-cyclic primes:	$5, 17$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7225$	$49773025$	$326657971600$	$2251016163765625$	$15516309295226355625$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$86$	$7220$	$571292$	$47431428$	$3939108706$	$326942537510$	$27136043176342$	$2252292060328708$	$186940256087853476$	$15516041200645798100$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 45 curves (of which all are hyperelliptic):

• $y^2=33 x^6+26 x^5+61 x^4+35 x^3+25 x^2+36 x+75$
• $y^2=8 x^6+x^5+48 x^4+23 x^3+9 x^2+41 x+68$
• $y^2=48 x^6+57 x^5+45 x^4+37 x^3+39 x^2+39 x+42$
• $y^2=66 x^6+24 x^5+36 x^4+70 x^3+36 x^2+24 x+66$
• $y^2=39 x^6+22 x^5+44 x^4+29 x^3+34 x^2+31 x+17$
• $y^2=18 x^6+65 x^5+64 x^4+67 x^3+78 x^2+80 x+70$
• $y^2=9 x^6+80 x^5+34 x^4+61 x^3+27 x^2+34 x+45$
• $y^2=66 x^6+78 x^5+33 x^4+54 x^3+80 x^2+10 x+77$
• $y^2=14 x^6+7 x^5+32 x^4+74 x^3+32 x^2+7 x+14$
• $y^2=40 x^6+52 x^5+81 x^4+28 x^3+81 x^2+52 x+40$
• $y^2=35 x^6+11 x^5+60 x^4+76 x^3+61 x^2+69 x+53$
• $y^2=6 x^6+78 x^5+54 x^4+70 x^3+70 x^2+50 x+43$
• $y^2=50 x^6+65 x^5+12 x^4+50 x^3+12 x^2+65 x+50$
• $y^2=65 x^6+13 x^5+10 x^4+39 x^3+47 x^2+62 x+77$
• $y^2=44 x^6+75 x^5+23 x^4+25 x^3+60 x^2+11 x+35$
• $y^2=18 x^6+71 x^5+21 x^4+11 x^3+56 x^2+79 x+46$
• $y^2=66 x^6+39 x^5+63 x^4+63 x^2+39 x+66$
• $y^2=60 x^6+29 x^5+21 x^4+74 x^3+21 x^2+29 x+60$
• $y^2=58 x^6+34 x^5+50 x^4+21 x^3+50 x^2+34 x+58$
• $y^2=17 x^6+75 x^5+12 x^4+67 x^3+76 x^2+10 x+30$
• and

• $y^2=6 x^6+81 x^5+24 x^4+63 x^3+40 x^2+21 x+47$
• $y^2=25 x^6+65 x^5+3 x^4+13 x^3+54 x^2+36 x+19$
• $y^2=75 x^6+54 x^5+16 x^4+75 x^3+75 x^2+76 x+8$
• $y^2=74 x^6+79 x^5+67 x^4+19 x^3+52 x^2+45 x+81$
• $y^2=24 x^6+53 x^5+32 x^4+78 x^3+32 x^2+53 x+24$
• $y^2=10 x^6+57 x^5+49 x^4+68 x^3+80 x^2+77 x+29$
• $y^2=46 x^6+78 x^5+71 x^4+75 x^3+71 x^2+78 x+46$
• $y^2=18 x^6+29 x^5+28 x^4+21 x^3+74 x+7$
• $y^2=19 x^6+58 x^5+68 x^4+59 x^3+82 x^2+58 x+16$
• $y^2=73 x^6+67 x^5+74 x^4+7 x^3+74 x^2+67 x+73$
• $y^2=33 x^6+35 x^5+5 x^4+54 x^3+20 x^2+24 x+19$
• $y^2=10 x^6+60 x^5+56 x^4+22 x^3+48 x^2+72 x+31$
• $y^2=78 x^6+72 x^5+82 x^4+29 x^3+46 x^2+15 x+19$
• $y^2=57 x^6+19 x^5+11 x^4+17 x^3+5 x^2+63 x+5$
• $y^2=69 x^6+41 x^5+6 x^4+63 x^3+x^2+49 x+7$
• $y^2=18 x^6+66 x^5+11 x^4+x^3+80 x^2+9 x+21$
• $y^2=72 x^6+61 x^5+28 x^4+47 x^3+76 x^2+42 x+58$
• $y^2=36 x^6+69 x^5+29 x^4+82 x^3+11 x^2+27 x+46$
• $y^2=42 x^6+71 x^5+41 x^4+24 x^2+82 x+63$
• $y^2=57 x^6+53 x^5+68 x^4+54 x^3+13 x^2+39 x+30$
• $y^2=4 x^6+55 x^5+81 x^4+8 x^3+35 x^2+64 x+23$
• $y^2=70 x^6+18 x^5+76 x^4+22 x^3+17 x^2+21 x+54$
• $y^2=53 x^6+76 x^5+52 x^4+28 x^3+52 x^2+76 x+53$
• $y^2=27 x^6+72 x^5+34 x^4+38 x^3+39 x^2+24 x+40$
• $y^2=61 x^6+75 x^5+8 x^4+8 x^3+8 x^2+75 x+61$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{83}$

The isogeny class factors as 1.83.b^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-331}) \)$)$

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.ac_gl	$2$	(not in LMFDB)
2.83.a_gj	$2$	(not in LMFDB)
2.83.ab_ade	$3$	(not in LMFDB)