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

• Label: 2.83.e_go
• 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:	$( 1 + 2 x + 83 x^{2} )^{2}$
	$1 + 4 x + 170 x^{2} + 332 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.535009590967$, $\pm0.535009590967$
Angle rank:	$1$ (numerical)
Jacobians:	$58$
Cyclic group of points:	no
Non-cyclic primes:	$2, 43$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7396$	$49730704$	$326381404804$	$2251109251572736$	$15516558017276212516$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$88$	$7214$	$570808$	$47433390$	$3939171848$	$326942180318$	$27136036485800$	$2252292111170014$	$186940256713296184$	$15516041194354771214$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 58 curves (of which all are hyperelliptic):

• $y^2=37 x^6+57 x^5+63 x^4+59 x^3+21 x^2+8 x+53$
• $y^2=35 x^6+54 x^5+57 x^4+25 x^3+82 x^2+56 x+66$
• $y^2=63 x^6+49 x^5+28 x^4+29 x^3+65 x^2+48 x+74$
• $y^2=63 x^6+7 x^5+80 x^4+2 x^3+64 x^2+41 x+77$
• $y^2=14 x^6+67 x^5+13 x^4+64 x^3+13 x^2+67 x+14$
• $y^2=13 x^6+69 x^5+7 x^4+53 x^3+10 x^2+17 x+56$
• $y^2=33 x^6+17 x^4+17 x^2+33$
• $y^2=60 x^6+53 x^5+38 x^4+51 x^3+48 x^2+55 x+62$
• $y^2=25 x^6+29 x^5+74 x^4+51 x^3+57 x^2+15 x+31$
• $y^2=51 x^6+27 x^5+70 x^4+12 x^3+66 x^2+73 x+4$
• $y^2=47 x^6+67 x^5+4 x^4+60 x^3+66 x^2+16 x+72$
• $y^2=76 x^6+32 x^5+79 x^4+23 x^3+79 x^2+32 x+76$
• $y^2=12 x^6+63 x^5+54 x^4+4 x^3+2 x^2+5 x+7$
• $y^2=7 x^6+35 x^5+4 x^4+5 x^3+4 x^2+35 x+7$
• $y^2=7 x^6+35 x^5+4 x^4+3 x^3+74 x^2+66 x+82$
• $y^2=80 x^6+13 x^5+41 x^4+60 x^3+39 x^2+76 x+25$
• $y^2=73 x^6+58 x^4+58 x^2+73$
• $y^2=11 x^6+45 x^5+30 x^4+37 x^3+18 x^2+66 x+59$
• $y^2=69 x^6+35 x^5+65 x^4+26 x^3+12 x^2+73 x+45$
• $y^2=8 x^6+5 x^5+31 x^4+16 x^3+65 x^2+13 x+57$
• and

• $y^2=31 x^6+60 x^5+66 x^4+74 x^3+74 x^2+30 x+61$
• $y^2=46 x^6+8 x^5+13 x^4+40 x^3+60 x^2+78 x+20$
• $y^2=72 x^6+28 x^5+31 x^4+30 x^3+28 x^2+52 x+54$
• $y^2=5 x^6+43 x^5+23 x^4+82 x^3+58 x^2+6 x+79$
• $y^2=53 x^6+14 x^5+69 x^4+66 x^3+64 x^2+8 x+14$
• $y^2=4 x^6+2 x^5+4 x^4+44 x^3+4 x^2+2 x+4$
• $y^2=43 x^6+13 x^5+63 x^4+72 x^3+66 x^2+43 x+65$
• $y^2=20 x^5+51 x^4+20 x^3+30 x^2+82 x+72$
• $y^2=75 x^6+9 x^5+14 x^4+71 x^3+17 x^2+3 x+74$
• $y^2=40 x^6+81 x^5+80 x^4+8 x^3+80 x^2+50 x+27$
• $y^2=79 x^6+70 x^5+6 x^4+39 x^3+54 x^2+12 x+60$
• $y^2=38 x^6+8 x^5+73 x^4+60 x^3+5 x^2+35 x+52$
• $y^2=74 x^6+32 x^5+x^4+3 x+44$
• $y^2=45 x^6+35 x^5+7 x^4+15 x^3+23 x^2+34 x+42$
• $y^2=36 x^6+29 x^5+39 x^4+70 x^3+39 x^2+29 x+36$
• $y^2=6 x^6+24 x^5+22 x^4+70 x^3+62 x^2+15 x+40$
• $y^2=67 x^6+76 x^5+44 x^4+50 x^3+3 x^2+53 x+60$
• $y^2=63 x^6+17 x^5+50 x^4+23 x^3+x^2+38 x+23$
• $y^2=73 x^5+17 x^4+35 x^3+17 x^2+73 x$
• $y^2=25 x^6+62 x^5+25 x^4+73 x^3+63 x^2+14 x+49$
• $y^2=40 x^6+42 x^5+59 x^4+34 x^3+63 x^2+52 x+66$
• $y^2=59 x^6+41 x^5+63 x^4+40 x^3+70 x^2+65 x+15$
• $y^2=43 x^6+7 x^5+48 x^4+78 x^3+73 x^2+70 x+77$
• $y^2=18 x^6+19 x^5+39 x^4+52 x^3+35 x^2+42$
• $y^2=32 x^6+47 x^5+9 x^4+5 x^3+68 x^2+60 x+24$
• $y^2=5 x^6+9 x^5+14 x^4+68 x^3+65 x^2+50 x$
• $y^2=x^6+23 x^5+76 x^4+2 x^3+27 x^2+21 x+74$
• $y^2=33 x^6+55 x^5+63 x^4+74 x^3+40 x^2+21 x+81$
• $y^2=12 x^6+53 x^5+17 x^4+50 x^3+43 x^2+28 x+24$
• $y^2=48 x^6+44 x^5+49 x^4+27 x^3+48 x^2+6 x+72$
• $y^2=10 x^6+9 x^5+23 x^4+13 x^3+79 x^2+39 x+59$
• $y^2=x^6+38 x^5+50 x^4+65 x^3+79 x^2+11 x+51$
• $y^2=53 x^6+12 x^5+15 x^4+28 x^3+15 x^2+12 x+53$
• $y^2=30 x^6+33 x^5+52 x^4+73 x^3+45 x^2+14 x+11$
• $y^2=2 x^6+65 x^5+41 x^4+45 x^3+42 x^2+4 x+27$
• $y^2=35 x^6+33 x^5+65 x^4+67 x^3+54 x^2+x+19$
• $y^2=6 x^6+34 x^5+7 x^4+57 x^3+3 x^2+45 x+6$
• $y^2=60 x^6+52 x^5+10 x^4+55 x^3+43 x^2+66 x+16$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{83}$

The isogeny class factors as 1.83.c^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-82}) \)$)$

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.ae_go	$2$	(not in LMFDB)
2.83.a_gg	$2$	(not in LMFDB)
2.83.ac_adb	$3$	(not in LMFDB)