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

• Label: 2.113.abb_nz
• 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:	$1 - 27 x + 363 x^{2} - 3051 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0996567331437$, $\pm0.396792718813$
Angle rank:	$2$ (numerical)
Number field:	4.0.570467293.1
Galois group:	$D_{4}$
Jacobians:	$46$
Isomorphism classes:	46

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10055$	$163001605$	$2082769945535$	$26582012415551125$	$339451716698563660400$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$87$	$12767$	$1443465$	$163032459$	$18424079202$	$2081951570639$	$235260589373421$	$26584442469610291$	$3004041940502260275$	$339456738992407067582$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 46 curves (of which all are hyperelliptic):

• $y^2=30 x^6+66 x^5+13 x^4+63 x^3+43 x^2+98 x+54$
• $y^2=98 x^6+23 x^5+35 x^4+17 x^3+105 x^2+12 x+6$
• $y^2=72 x^6+103 x^5+87 x^4+21 x^3+45 x^2+106 x+14$
• $y^2=50 x^6+58 x^5+92 x^4+5 x^3+111 x^2+69 x+48$
• $y^2=50 x^6+x^5+3 x^4+96 x^3+94 x^2+27 x+35$
• $y^2=76 x^6+86 x^5+6 x^4+43 x^3+51 x^2+111 x+94$
• $y^2=107 x^6+81 x^5+40 x^4+3 x^3+109 x^2+63 x+100$
• $y^2=47 x^6+73 x^5+20 x^4+76 x^3+10 x^2+33 x+73$
• $y^2=6 x^6+100 x^5+92 x^4+30 x^3+98 x^2+41 x+58$
• $y^2=107 x^6+9 x^5+72 x^4+100 x^3+92 x^2+101 x+107$
• $y^2=86 x^6+38 x^5+76 x^4+92 x^3+18 x^2+5 x+23$
• $y^2=101 x^6+109 x^5+83 x^4+62 x^3+61 x^2+63 x+107$
• $y^2=72 x^6+46 x^5+23 x^4+51 x^2+44$
• $y^2=12 x^6+37 x^5+50 x^4+109 x^3+80 x^2+15 x+40$
• $y^2=96 x^6+75 x^5+103 x^4+97 x^3+41 x^2+57 x+42$
• $y^2=50 x^6+79 x^5+54 x^4+72 x^3+69 x^2+11 x+79$
• $y^2=103 x^6+79 x^5+26 x^4+87 x^3+56 x^2+26 x+103$
• $y^2=61 x^6+95 x^5+94 x^4+46 x^3+35 x^2+8 x+45$
• $y^2=67 x^6+97 x^5+6 x^4+50 x^3+18 x^2+27 x+55$
• $y^2=58 x^6+94 x^5+94 x^4+100 x^3+50 x^2+33 x+75$
• and

• $y^2=107 x^6+109 x^5+28 x^4+48 x^3+15 x^2+34 x+42$
• $y^2=71 x^6+16 x^5+26 x^4+53 x^3+69 x^2+93 x+12$
• $y^2=53 x^6+72 x^5+84 x^4+35 x^3+39 x^2+20 x+65$
• $y^2=106 x^6+44 x^5+5 x^4+6 x^3+48 x^2+42 x+48$
• $y^2=107 x^6+80 x^5+24 x^4+75 x^3+67 x^2+7 x+29$
• $y^2=111 x^6+21 x^5+69 x^4+91 x^3+53 x^2+20 x+101$
• $y^2=63 x^6+55 x^5+71 x^4+49 x^3+72 x^2+18 x+31$
• $y^2=62 x^6+102 x^5+76 x^4+7 x^3+81 x^2+24 x+69$
• $y^2=65 x^6+32 x^5+45 x^4+65 x^3+26 x^2+32 x+37$
• $y^2=93 x^6+34 x^5+99 x^4+6 x^3+100 x^2+106 x+50$
• $y^2=46 x^6+32 x^5+39 x^4+109 x^3+28 x^2+15 x+110$
• $y^2=56 x^6+82 x^5+10 x^4+22 x^3+21 x^2+x+68$
• $y^2=75 x^6+107 x^5+83 x^4+28 x^3+81 x^2+104 x+33$
• $y^2=53 x^6+47 x^5+75 x^4+48 x^3+112 x^2+75 x+24$
• $y^2=54 x^6+100 x^5+99 x^4+16 x^3+66 x^2+21 x+105$
• $y^2=5 x^6+98 x^5+101 x^4+89 x^3+9 x^2+107 x+14$
• $y^2=44 x^6+47 x^5+77 x^4+26 x^3+5 x^2+104 x+17$
• $y^2=40 x^6+92 x^5+36 x^4+55 x^3+56 x^2+6 x+92$
• $y^2=43 x^6+77 x^5+107 x^4+30 x^3+11 x^2+78 x+26$
• $y^2=31 x^6+89 x^5+52 x^4+2 x^3+109 x^2+12 x+36$
• $y^2=78 x^6+30 x^5+82 x^4+16 x^3+59 x^2+9 x+61$
• $y^2=107 x^6+91 x^5+85 x^4+108 x^3+102 x^2+34 x+110$
• $y^2=42 x^5+104 x^4+89 x^3+20 x^2+83 x+81$
• $y^2=21 x^6+104 x^5+63 x^4+28 x^3+89 x^2+109 x+92$
• $y^2=74 x^6+45 x^5+87 x^4+5 x^3+104 x^2+46 x+84$
• $y^2=92 x^6+89 x^5+30 x^4+97 x^3+2 x^2+66 x+43$

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 4.0.570467293.1.

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.bb_nz	$2$	(not in LMFDB)