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

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

Invariants

Base field:	$\F_{83}$
Dimension:	$2$
L-polynomial:	$1 - 11 x + 38 x^{2} - 913 x^{3} + 6889 x^{4}$
Frobenius angles:	$\pm0.0396422182658$, $\pm0.627024448401$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-3}, \sqrt{-211})\)
Galois group:	$C_2^2$
Jacobians:	$57$

This isogeny class is simple but not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6004$	$47143408$	$325333344400$	$2251734545155264$	$15516090102366802204$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$73$	$6845$	$568972$	$47446569$	$3939053063$	$326938695590$	$27136040731061$	$2252292275355409$	$186940254515378356$	$15516041179482003725$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 57 curves (of which all are hyperelliptic):

• $y^2=17 x^6+16 x^5+24 x^4+8 x^3+74 x^2+37 x+58$
• $y^2=66 x^6+79 x^5+38 x^4+43 x^3+8 x^2+16 x+35$
• $y^2=78 x^6+41 x^5+48 x^4+20 x^3+29 x^2+48 x+68$
• $y^2=72 x^6+5 x^5+58 x^4+73 x^3+6 x^2+15 x+70$
• $y^2=14 x^6+25 x^5+39 x^4+49 x^3+40 x^2+76 x+62$
• $y^2=13 x^6+78 x^5+68 x^4+57 x^3+53 x^2+25 x+15$
• $y^2=66 x^6+67 x^5+72 x^4+x^3+75 x^2+35 x+34$
• $y^2=24 x^6+71 x^5+52 x^4+55 x^3+57 x^2+45 x+76$
• $y^2=60 x^6+6 x^5+47 x^4+73 x^3+29 x^2+5 x+55$
• $y^2=73 x^6+82 x^5+67 x^4+64 x^3+30 x^2+2 x+15$
• $y^2=82 x^6+40 x^5+9 x^4+32 x^3+23 x^2+69 x+26$
• $y^2=19 x^6+35 x^5+47 x^4+2 x^3+81 x^2+69 x+5$
• $y^2=59 x^6+23 x^5+64 x^4+62 x^3+52 x^2+79 x+67$
• $y^2=32 x^6+28 x^5+68 x^4+34 x^3+33 x^2+11 x+5$
• $y^2=55 x^6+51 x^5+38 x^4+27 x^3+44 x^2+64 x+61$
• $y^2=60 x^6+8 x^5+54 x^3+5 x^2+46 x+67$
• $y^2=50 x^5+25 x^4+70 x^3+81 x^2+49 x+79$
• $y^2=27 x^6+46 x^5+47 x^4+71 x^3+5 x^2+2 x+27$
• $y^2=76 x^6+32 x^5+26 x^4+74 x^3+3 x^2+76 x+68$
• $y^2=82 x^6+4 x^5+5 x^4+73 x^3+78 x^2+19 x+1$
• and

• $y^2=74 x^6+13 x^5+81 x^4+68 x^3+3 x^2+9 x+19$
• $y^2=56 x^6+49 x^5+48 x^4+44 x^3+21 x^2+23 x+22$
• $y^2=23 x^6+7 x^5+33 x^4+16 x^3+63 x^2+74 x+4$
• $y^2=15 x^6+16 x^5+14 x^4+11 x^3+22 x^2+55 x+66$
• $y^2=20 x^6+79 x^5+8 x^4+40 x^3+29 x^2+16 x+60$
• $y^2=81 x^6+66 x^5+57 x^4+64 x^3+72 x^2+27 x+5$
• $y^2=41 x^6+14 x^5+79 x^4+58 x^3+17 x^2+59 x+45$
• $y^2=44 x^6+3 x^5+47 x^4+44 x^3+71 x^2+34 x+60$
• $y^2=80 x^6+57 x^5+26 x^4+5 x^3+9 x^2+13 x+15$
• $y^2=49 x^6+70 x^5+68 x^4+72 x^3+40 x^2+11 x+36$
• $y^2=17 x^6+69 x^5+7 x^4+51 x^3+69 x^2+13 x+79$
• $y^2=42 x^6+19 x^5+14 x^4+33 x^3+41 x^2+53 x+7$
• $y^2=70 x^6+25 x^5+66 x^4+45 x^3+45 x^2+28 x+74$
• $y^2=11 x^6+64 x^5+79 x^4+72 x^3+43 x^2+60 x+1$
• $y^2=79 x^6+41 x^5+50 x^4+52 x^3+65 x^2+57 x+1$
• $y^2=34 x^6+46 x^5+78 x^4+36 x^3+35 x^2+61 x+42$
• $y^2=56 x^6+2 x^5+58 x^4+12 x^3+31 x^2+71 x+38$
• $y^2=6 x^6+66 x^5+76 x^4+65 x^3+56 x^2+57 x+8$
• $y^2=32 x^6+24 x^5+64 x^4+63 x^3+27 x^2+69 x+23$
• $y^2=75 x^6+80 x^5+70 x^4+6 x^3+25 x^2+43 x+7$
• $y^2=54 x^6+10 x^5+62 x^4+21 x^3+5 x^2+20 x+33$
• $y^2=76 x^6+54 x^5+14 x^4+51 x^3+14 x^2+72 x+47$
• $y^2=63 x^6+33 x^5+55 x^4+37 x^3+17 x^2+29 x+80$
• $y^2=3 x^6+37 x^5+66 x^4+48 x^3+58 x^2+3 x+11$
• $y^2=47 x^6+69 x^5+26 x^4+35 x^3+29 x^2+8 x+5$
• $y^2=71 x^6+35 x^5+61 x^4+33 x^3+13 x^2+66 x+74$
• $y^2=67 x^6+16 x^5+64 x^4+65 x^3+19 x^2+75 x+67$
• $y^2=66 x^6+71 x^5+12 x^4+46 x^3+54 x^2+69 x+54$
• $y^2=15 x^6+74 x^5+31 x^4+2 x^3+54 x^2+69 x+65$
• $y^2=55 x^6+51 x^5+55 x^4+58 x^3+76 x^2+49 x+76$
• $y^2=29 x^6+2 x^5+80 x^4+4 x^3+28 x^2+24 x+29$
• $y^2=62 x^6+55 x^5+6 x^4+28 x^3+39 x^2+59 x+45$
• $y^2=12 x^6+32 x^5+48 x^4+69 x^3+69 x^2+66 x+22$
• $y^2=18 x^6+13 x^5+49 x^4+46 x^3+57 x^2+54 x+55$
• $y^2=58 x^6+35 x^5+49 x^4+49 x^3+61 x^2+55 x+12$
• $y^2=70 x^6+64 x^5+23 x^4+27 x^3+43 x^2+60 x+25$
• $y^2=71 x^6+34 x^5+8 x^4+4 x^3+69 x^2+81 x+79$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{83^{3}}$.

Endomorphism algebra over $\F_{83}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}, \sqrt{-211})\).

Endomorphism algebra over $\overline{\F}_{83}$

The base change of $A$ to $\F_{83^{3}}$ is 1.571787.acce^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-211}) \)$)$

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.l_bm	$2$	(not in LMFDB)
2.83.w_lb	$3$	(not in LMFDB)
2.83.aw_lb	$6$	(not in LMFDB)