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

• Label: 2.113.av_jd
• 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:	$1 - 21 x + 237 x^{2} - 2373 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0874806695974$, $\pm0.491950615215$
Angle rank:	$2$ (numerical)
Number field:	4.0.2369966533.1
Galois group:	$D_{4}$
Jacobians:	$42$
Isomorphism classes:	42

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$10613$	$163450813$	$2079863582213$	$26578408656148309$	$339455131027159675088$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$93$	$12803$	$1441449$	$163010355$	$18424264518$	$2081954830619$	$235260564052089$	$26584441801165315$	$3004041939923208501$	$339456739061934281438$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 42 curves (of which all are hyperelliptic):

• $y^2=13 x^6+82 x^5+109 x^4+32 x^3+59 x^2+89 x+49$
• $y^2=74 x^6+97 x^5+80 x^4+55 x^3+65 x^2+75 x+112$
• $y^2=33 x^6+58 x^5+44 x^4+111 x^3+67 x^2+96 x+103$
• $y^2=2 x^6+59 x^5+86 x^4+49 x^3+83 x^2+49 x+93$
• $y^2=101 x^6+26 x^5+41 x^4+41 x^3+97 x^2+33 x+63$
• $y^2=77 x^6+71 x^5+30 x^4+70 x^3+16 x^2+60 x+1$
• $y^2=31 x^6+78 x^5+72 x^4+89 x^3+71 x^2+51 x+112$
• $y^2=71 x^6+96 x^5+72 x^4+33 x^3+53 x^2+77 x+37$
• $y^2=50 x^6+97 x^5+13 x^4+16 x^3+27 x^2+5 x+32$
• $y^2=98 x^6+55 x^5+43 x^4+58 x^3+39 x^2+59 x+105$
• $y^2=5 x^6+32 x^5+86 x^4+77 x^3+92 x^2+79 x+49$
• $y^2=21 x^6+82 x^5+36 x^4+48 x^3+68 x^2+43 x+45$
• $y^2=47 x^6+80 x^5+73 x^4+31 x^3+23 x^2+81 x+97$
• $y^2=21 x^6+53 x^5+104 x^4+29 x^3+48 x^2+23 x+27$
• $y^2=8 x^6+6 x^5+63 x^4+52 x^3+5 x^2+95 x+7$
• $y^2=31 x^6+10 x^5+78 x^4+67 x^3+x^2+89 x+87$
• $y^2=17 x^6+7 x^5+71 x^4+39 x^3+96 x^2+6 x+100$
• $y^2=79 x^6+111 x^5+59 x^4+28 x^3+19 x^2+30 x+15$
• $y^2=91 x^6+65 x^5+x^4+80 x^3+21 x^2+94 x+93$
• $y^2=39 x^6+69 x^5+62 x^4+70 x^3+46 x^2+112 x+18$
• and

• $y^2=30 x^6+17 x^5+62 x^4+64 x^3+109 x^2+2 x+16$
• $y^2=27 x^6+15 x^5+74 x^4+19 x^3+47 x^2+42 x+29$
• $y^2=17 x^6+103 x^5+109 x^4+44 x^3+81 x^2+63 x+71$
• $y^2=74 x^6+70 x^5+4 x^4+82 x^3+99 x^2+x+21$
• $y^2=35 x^6+54 x^5+105 x^4+104 x^3+62 x^2+95 x+18$
• $y^2=111 x^6+36 x^5+86 x^4+18 x^3+4 x^2+10 x+77$
• $y^2=18 x^6+55 x^5+92 x^4+3 x^3+107 x^2+19 x+80$
• $y^2=26 x^6+3 x^5+59 x^4+15 x^3+98 x^2+24 x+45$
• $y^2=34 x^6+54 x^5+67 x^4+34 x^3+91 x^2+31 x+16$
• $y^2=85 x^5+48 x^4+30 x^3+44 x^2+50 x+24$
• $y^2=74 x^6+4 x^5+91 x^4+48 x^3+44 x^2+44 x+58$
• $y^2=46 x^6+20 x^5+88 x^4+90 x^3+7 x^2+13 x+66$
• $y^2=78 x^6+44 x^5+81 x^4+32 x^3+34 x^2+89 x+46$
• $y^2=67 x^6+44 x^5+84 x^4+107 x^3+6 x^2+68 x+85$
• $y^2=96 x^6+58 x^5+19 x^4+106 x^3+20 x^2+74 x+50$
• $y^2=30 x^6+71 x^5+106 x^4+28 x^3+46 x^2+20 x+61$
• $y^2=99 x^6+112 x^5+51 x^4+41 x^3+86 x^2+97 x+82$
• $y^2=61 x^6+99 x^5+10 x^4+45 x^3+20 x^2+38 x+29$
• $y^2=42 x^6+27 x^5+85 x^4+55 x^3+45 x^2+111 x+53$
• $y^2=x^6+26 x^5+85 x^4+10 x^3+99 x^2+41 x+89$
• $y^2=6 x^6+32 x^5+10 x^4+6 x^3+48 x^2+19 x+94$
• $y^2=76 x^6+29 x^5+63 x^4+10 x^3+19 x^2+97 x+72$

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 4.0.2369966533.1.

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.v_jd	$2$	(not in LMFDB)