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

• Label: 2.83.m_he
• 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:	$( 1 + 2 x + 83 x^{2} )( 1 + 10 x + 83 x^{2} )$
	$1 + 12 x + 186 x^{2} + 996 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.535009590967$, $\pm0.684923259698$
Angle rank:	$2$ (numerical)
Jacobians:	$64$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8084$	$49053712$	$325810106804$	$2252147746468864$	$15516415610707207124$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$96$	$7118$	$569808$	$47455278$	$3939135696$	$326940200318$	$27136052058624$	$2252292177797086$	$186940255238357184$	$15516041197791091118$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 64 curves (of which all are hyperelliptic):

• $y^2=73 x^6+29 x^5+75 x^4+62 x^3+13 x^2+81 x+59$
• $y^2=33 x^6+53 x^5+64 x^4+4 x^3+5 x^2+45 x+7$
• $y^2=15 x^6+14 x^5+40 x^4+8 x^3+25 x^2+70 x+62$
• $y^2=82 x^6+28 x^5+26 x^4+21 x^3+26 x^2+28 x+82$
• $y^2=71 x^6+7 x^5+7 x^4+4 x^3+58 x^2+56 x+42$
• $y^2=50 x^6+71 x^5+40 x^4+21 x^3+61 x^2+49 x+16$
• $y^2=8 x^6+16 x^5+74 x^4+23 x^3+31 x^2+12 x+40$
• $y^2=7 x^6+44 x^5+56 x^4+49 x^3+13 x^2+48 x+81$
• $y^2=4 x^6+29 x^5+7 x^4+47 x^3+32 x^2+20 x+62$
• $y^2=18 x^6+49 x^5+63 x^4+50 x^3+12 x^2+11 x+24$
• $y^2=76 x^6+35 x^5+26 x^4+17 x^3+16 x^2+30 x+4$
• $y^2=42 x^6+59 x^5+76 x^4+2 x^3+44 x^2+17 x+49$
• $y^2=25 x^6+66 x^5+47 x^4+6 x^3+15 x^2+8 x+70$
• $y^2=18 x^6+38 x^5+35 x^4+3 x^3+3 x^2+48 x+72$
• $y^2=23 x^6+24 x^5+37 x^4+50 x^3+50 x^2+61 x+46$
• $y^2=61 x^6+31 x^5+66 x^3+18 x^2+16 x+66$
• $y^2=58 x^6+24 x^5+41 x^4+21 x^3+23 x^2+54 x+55$
• $y^2=63 x^6+56 x^5+60 x^4+33 x^3+12 x^2+32 x+79$
• $y^2=33 x^6+28 x^5+57 x^4+9 x^3+x^2+60 x+70$
• $y^2=7 x^6+7 x^5+x^4+44 x^3+2 x^2+75 x+35$
• and

• $y^2=56 x^6+50 x^5+78 x^4+51 x^3+26 x^2+40 x+2$
• $y^2=41 x^6+43 x^5+47 x^4+71 x^3+56 x^2+19 x+16$
• $y^2=76 x^6+26 x^5+67 x^4+41 x^3+52 x^2+25 x+70$
• $y^2=75 x^6+34 x^5+67 x^4+22 x^3+67 x^2+34 x+75$
• $y^2=69 x^6+10 x^5+5 x^4+17 x^3+44 x^2+5 x+2$
• $y^2=79 x^6+7 x^5+37 x^4+13 x^3+37 x^2+7 x+79$
• $y^2=35 x^6+71 x^5+73 x^4+78 x^3+8 x^2+67 x+73$
• $y^2=61 x^6+43 x^4+19 x^3+65 x^2+66 x+45$
• $y^2=63 x^6+43 x^5+73 x^4+79 x^3+58 x^2+82 x+61$
• $y^2=7 x^6+40 x^5+13 x^4+18 x^3+18 x^2+44 x+39$
• $y^2=51 x^6+7 x^5+57 x^4+12 x^3+24 x^2+32 x+55$
• $y^2=67 x^6+16 x^5+51 x^4+45 x^3+81 x^2+15 x+27$
• $y^2=17 x^6+81 x^5+75 x^4+33 x^3+75 x^2+25 x+1$
• $y^2=12 x^6+66 x^5+23 x^3+27 x^2+15 x+3$
• $y^2=41 x^6+39 x^5+56 x^4+29 x^3+36 x^2+77 x+74$
• $y^2=41 x^6+81 x^5+68 x^4+63 x^3+68 x^2+81 x+41$
• $y^2=44 x^6+51 x^5+12 x^4+40 x^3+41 x^2+35 x+62$
• $y^2=63 x^6+58 x^5+51 x^4+12 x^3+13 x^2+39 x+27$
• $y^2=7 x^6+68 x^5+36 x^4+78 x^3+11 x^2+23 x+82$
• $y^2=8 x^6+57 x^5+39 x^4+57 x^3+25 x^2+29 x+39$
• $y^2=2 x^6+36 x^5+75 x^4+72 x^3+81 x^2+23 x+13$
• $y^2=29 x^6+28 x^5+82 x^4+44 x^3+28 x^2+13 x+26$
• $y^2=77 x^6+61 x^5+33 x^4+35 x^3+33 x^2+61 x+77$
• $y^2=16 x^6+37 x^5+76 x^4+28 x^3+26 x^2+55 x+24$
• $y^2=19 x^6+3 x^5+9 x^4+26 x^3+71 x^2+5 x+5$
• $y^2=26 x^6+73 x^5+11 x^4+68 x^3+11 x^2+73 x+26$
• $y^2=63 x^6+76 x^5+41 x^4+45 x^3+41 x^2+76 x+63$
• $y^2=65 x^6+81 x^5+44 x^4+27 x^3+77 x^2+25 x+41$
• $y^2=65 x^6+70 x^5+65 x^4+3 x^3+12 x^2+31 x+36$
• $y^2=74 x^6+4 x^5+61 x^4+49 x^3+28 x^2+27 x+57$
• $y^2=6 x^6+58 x^5+12 x^4+82 x^3+45 x^2+50 x+66$
• $y^2=21 x^6+69 x^5+30 x^4+6 x^2+82 x+12$
• $y^2=48 x^6+28 x^5+15 x^4+73 x^3+58 x^2+32 x+65$
• $y^2=2 x^6+38 x^5+8 x^4+21 x^3+18 x^2+16 x+15$
• $y^2=23 x^6+61 x^5+33 x^4+8 x^3+2 x^2+58 x+35$
• $y^2=30 x^5+48 x^4+7 x^3+48 x^2+30 x$
• $y^2=13 x^6+26 x^5+53 x^4+15 x^3+53 x^2+27 x+71$
• $y^2=80 x^6+40 x^5+33 x^4+10 x^3+55 x^2+59 x+67$
• $y^2=47 x^6+33 x^5+52 x^4+66 x^3+67 x^2+35 x+69$
• $y^2=62 x^6+16 x^5+40 x^4+66 x^3+71 x^2+54 x+43$
• $y^2=42 x^6+73 x^5+39 x^4+19 x^3+44 x^2+14 x+82$
• $y^2=10 x^6+72 x^5+62 x^4+16 x^3+65 x+30$
• $y^2=38 x^6+19 x^5+67 x^4+4 x^3+34 x^2+27 x+2$
• $y^2=79 x^6+47 x^5+57 x^4+23 x^3+37 x^2+42 x+15$

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 $\times$ 1.83.k and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.83.c : \(\Q(\sqrt{-82}) \).
• 1.83.k : \(\Q(\sqrt{-58}) \).

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.am_he	$2$	(not in LMFDB)
2.83.ai_fq	$2$	(not in LMFDB)
2.83.i_fq	$2$	(not in LMFDB)