Abelian variety isogeny class 2.113.abg_rw over $\F_{113}$

• Label: 2.113.abg_rw
• Base field: $\F_{113}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{113}$
Dimension:	$2$
L-polynomial:	$1 - 32 x + 464 x^{2} - 3616 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0988843764289$, $\pm0.313475432574$
Angle rank:	$2$ (numerical)
Number field:	4.0.848128.2
Galois group:	$D_{4}$
Jacobians:	$36$
Isomorphism classes:	36

This isogeny class is simple and 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9586$	$161830852$	$2083290266482$	$26586008015213584$	$339455600551796283826$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$82$	$12674$	$1443826$	$163056966$	$18424290002$	$2081949900482$	$235260540326642$	$26584442195396734$	$3004041944179866322$	$339456739062644111234$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 36 curves (of which all are hyperelliptic):

• $y^2=40 x^6+86 x^5+29 x^4+83 x^3+20 x^2+5 x+48$
• $y^2=110 x^6+77 x^5+89 x^4+71 x^3+75 x^2+11 x+105$
• $y^2=5 x^6+47 x^5+9 x^4+79 x^3+109 x^2+12 x+100$
• $y^2=5 x^6+15 x^5+103 x^4+75 x^3+5 x^2+4 x+53$
• $y^2=65 x^6+69 x^5+35 x^4+60 x^3+90 x^2+43 x+29$
• $y^2=101 x^6+102 x^5+46 x^4+17 x^3+108 x^2+78 x+12$
• $y^2=44 x^6+26 x^5+74 x^4+27 x^3+16 x^2+57 x+101$
• $y^2=18 x^6+94 x^5+45 x^4+82 x^3+17 x^2+101 x+55$
• $y^2=72 x^6+66 x^5+34 x^4+82 x^3+90 x+73$
• $y^2=40 x^6+90 x^5+86 x^4+88 x^3+105 x^2+72 x+6$
• $y^2=61 x^6+105 x^5+104 x^4+52 x^3+82 x^2+73 x+23$
• $y^2=47 x^6+101 x^5+61 x^4+21 x^3+96 x^2+17 x+103$
• $y^2=56 x^6+47 x^4+94 x^3+7 x^2+17 x+21$
• $y^2=20 x^6+96 x^5+17 x^4+110 x^3+96 x^2+83 x+110$
• $y^2=63 x^6+31 x^5+35 x^4+13 x^3+37 x^2+15 x+106$
• $y^2=23 x^6+10 x^5+29 x^4+56 x^3+3 x^2+79 x+59$
• $y^2=59 x^6+63 x^5+104 x^4+70 x^3+48 x^2+35 x+74$
• $y^2=19 x^6+62 x^5+9 x^4+54 x^3+5 x^2+7 x+28$
• $y^2=80 x^6+43 x^5+17 x^4+75 x^3+92 x^2+48 x+86$
• $y^2=40 x^6+33 x^5+68 x^4+75 x^3+51 x^2+34 x+90$
• and

• $y^2=45 x^6+78 x^5+73 x^4+58 x^3+8 x^2+15 x+20$
• $y^2=95 x^6+46 x^5+21 x^4+47 x^3+62 x^2+109 x+104$
• $y^2=69 x^6+16 x^5+88 x^4+91 x^3+34 x^2+23 x+41$
• $y^2=37 x^6+46 x^5+33 x^4+29 x^3+107 x^2+63 x+10$
• $y^2=41 x^6+98 x^5+11 x^4+25 x^3+41 x^2+11 x+15$
• $y^2=48 x^6+81 x^5+99 x^4+56 x^3+4 x^2+82 x+110$
• $y^2=92 x^6+32 x^5+72 x^4+25 x^3+72 x^2+54 x+60$
• $y^2=59 x^6+48 x^5+65 x^4+32 x^3+65 x^2+75 x+47$
• $y^2=63 x^6+87 x^5+41 x^4+59 x^3+17 x^2+96 x+100$
• $y^2=32 x^6+52 x^5+61 x^4+88 x^3+5 x^2+37 x+1$
• $y^2=26 x^6+8 x^5+60 x^4+110 x^3+72 x^2+54 x+51$
• $y^2=27 x^6+89 x^5+109 x^4+76 x^3+22 x^2+107 x+41$
• $y^2=107 x^6+14 x^5+46 x^4+34 x^3+45 x^2+63 x+108$
• $y^2=87 x^6+70 x^5+34 x^4+24 x^3+31 x^2+101 x+10$
• $y^2=95 x^6+19 x^5+23 x^4+24 x^3+34 x^2+93 x+95$
• $y^2=67 x^6+66 x^5+66 x^4+54 x^3+3 x^2+25 x+46$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{113}$.

Endomorphism algebra over $\F_{113}$

The endomorphism algebra of this simple isogeny class is 4.0.848128.2.

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
2.113.bg_rw	$2$	(not in LMFDB)