Abelian variety isogeny class 2.101.abg_rh over $\F_{101}$

• Label: 2.101.abg_rh
• Base field: $\F_{101}$
• 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:	$\F_{101}$
Dimension:	$2$
L-polynomial:	$( 1 - 19 x + 101 x^{2} )( 1 - 13 x + 101 x^{2} )$
	$1 - 32 x + 449 x^{2} - 3232 x^{3} + 10201 x^{4}$
Frobenius angles:	$\pm0.105783363728$, $\pm0.276117624376$
Angle rank:	$2$ (numerical)
Jacobians:	$22$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7387$	$102790105$	$1062179684800$	$10830069178015945$	$110463197654237940787$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$70$	$10076$	$1030942$	$104074836$	$10510194230$	$1061520022838$	$107213529160430$	$10828567075725796$	$1093685274654120262$	$110462212577170789676$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 22 curves (of which all are hyperelliptic):

• $y^2=31 x^6+16 x^5+17 x^4+34 x^3+2 x^2+80 x+72$
• $y^2=3 x^6+49 x^5+50 x^4+90 x^3+15 x^2+80 x+77$
• $y^2=75 x^6+13 x^5+72 x^4+75 x^3+52 x+43$
• $y^2=7 x^6+100 x^5+66 x^4+75 x^3+26 x^2+44 x+90$
• $y^2=12 x^6+55 x^5+20 x^4+88 x^3+20 x^2+55 x+12$
• $y^2=87 x^6+90 x^5+32 x^4+97 x^3+81 x^2+86 x+30$
• $y^2=8 x^6+80 x^5+96 x^4+65 x^3+37 x^2+8 x+34$
• $y^2=8 x^6+66 x^5+20 x^4+9 x^3+15 x^2+60 x+63$
• $y^2=40 x^6+45 x^5+95 x^4+22 x^3+95 x^2+45 x+40$
• $y^2=44 x^6+96 x^5+24 x^4+5 x^3+83 x^2+19 x+12$
• $y^2=91 x^6+57 x^5+49 x^4+93 x^3+45 x^2+62 x+64$
• $y^2=29 x^6+38 x^5+21 x^4+67 x^3+21 x^2+38 x+29$
• $y^2=58 x^6+5 x^5+64 x^4+49 x^3+54 x^2+33 x+74$
• $y^2=47 x^6+14 x^5+31 x^4+100 x^3+46 x^2+64 x+51$
• $y^2=48 x^6+43 x^5+15 x^4+11 x^3+15 x^2+43 x+48$
• $y^2=77 x^6+10 x^5+54 x^4+68 x^3+72 x^2+x+90$
• $y^2=91 x^6+2 x^5+69 x^4+3 x^3+69 x^2+2 x+91$
• $y^2=37 x^6+12 x^5+80 x^4+9 x^3+51 x^2+81 x+1$
• $y^2=46 x^6+87 x^5+23 x^4+28 x^3+67 x^2+7 x+61$
• $y^2=28 x^6+43 x^5+24 x^4+27 x^3+67 x^2+91 x+97$
• $y^2=x^6+87 x^5+28 x^4+88 x^3+78 x^2+45 x+72$
• $y^2=89 x^6+78 x^5+83 x^4+88 x^3+83 x^2+78 x+89$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{101}$.

Endomorphism algebra over $\F_{101}$

The isogeny class factors as 1.101.at $\times$ 1.101.an and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.101.at : \(\Q(\sqrt{-43}) \).
• 1.101.an : \(\Q(\sqrt{-235}) \).

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
2.101.ag_abt	$2$	(not in LMFDB)
2.101.g_abt	$2$	(not in LMFDB)
2.101.bg_rh	$2$	(not in LMFDB)