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

• Label: 2.113.abe_rb
• 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:	$1 - 30 x + 443 x^{2} - 3390 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.183387034006$, $\pm0.305972628890$
Angle rank:	$2$ (numerical)
Number field:	4.0.2608704.1
Galois group:	$D_{4}$
Jacobians:	$48$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9793$	$162886969$	$2085851338816$	$26590406534642601$	$339461102830123177393$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$84$	$12756$	$1445598$	$163083940$	$18424588644$	$2081951985822$	$235260539639748$	$26584441909456324$	$3004041938885725374$	$339456738996481299636$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 48 curves (of which all are hyperelliptic):

• $y^2=68 x^6+x^5+83 x^4+54 x^3+x^2+112 x+43$
• $y^2=64 x^6+45 x^5+18 x^4+49 x^3+45 x^2+33 x+38$
• $y^2=34 x^6+33 x^5+5 x^4+86 x^3+93 x^2+77 x+104$
• $y^2=2 x^6+101 x^5+39 x^4+85 x^3+78 x^2+93 x+28$
• $y^2=44 x^6+77 x^5+111 x^4+96 x^3+72 x^2+38 x+18$
• $y^2=54 x^6+45 x^5+31 x^4+52 x^3+8 x^2+15 x+70$
• $y^2=93 x^6+30 x^5+6 x^4+64 x^3+84 x^2+51 x+40$
• $y^2=39 x^6+109 x^5+7 x^4+95 x^3+9 x^2+22 x+19$
• $y^2=28 x^6+5 x^5+56 x^4+9 x^3+73 x^2+99 x+31$
• $y^2=74 x^6+61 x^5+28 x^4+51 x^3+54 x^2+12 x+67$
• $y^2=37 x^6+41 x^5+90 x^4+86 x^3+34 x^2+46 x+45$
• $y^2=43 x^6+12 x^5+70 x^4+57 x^3+61 x^2+2 x+28$
• $y^2=34 x^6+96 x^5+7 x^4+7 x^3+51 x^2+7 x+92$
• $y^2=65 x^6+17 x^5+11 x^4+17 x^3+59 x^2+84$
• $y^2=100 x^6+74 x^5+71 x^4+86 x^3+106 x^2+32 x+29$
• $y^2=55 x^6+108 x^5+97 x^4+24 x^3+66 x^2+44 x+68$
• $y^2=62 x^6+84 x^5+30 x^4+30 x^3+45 x^2+30 x+103$
• $y^2=29 x^6+22 x^5+94 x^4+25 x^3+60 x^2+62 x+82$
• $y^2=103 x^6+99 x^5+99 x^3+40 x^2+28 x+23$
• $y^2=6 x^6+30 x^5+38 x^4+28 x^3+25 x^2+75 x+103$
• and

• $y^2=84 x^6+58 x^5+98 x^4+12 x^3+40 x^2+81 x+7$
• $y^2=78 x^6+2 x^5+82 x^4+76 x^3+16 x^2+104 x+82$
• $y^2=92 x^6+31 x^5+62 x^4+104 x^3+47 x^2+112 x+44$
• $y^2=107 x^6+43 x^5+107 x^4+30 x^3+111 x^2+111 x+87$
• $y^2=72 x^6+106 x^5+71 x^4+41 x^3+8 x^2+103 x+83$
• $y^2=107 x^6+88 x^5+101 x^4+4 x^3+31 x^2+48 x+59$
• $y^2=34 x^6+3 x^5+89 x^4+46 x^3+45 x^2+79 x+80$
• $y^2=46 x^6+80 x^5+66 x^4+99 x^3+51 x^2+78 x+67$
• $y^2=15 x^6+101 x^5+101 x^4+35 x^3+72 x^2+108 x+19$
• $y^2=87 x^6+95 x^5+10 x^4+58 x^3+48 x^2+62 x+34$
• $y^2=92 x^6+38 x^5+42 x^4+50 x^3+14 x^2+68 x+42$
• $y^2=109 x^6+40 x^5+110 x^4+78 x^3+10 x^2+62 x+26$
• $y^2=11 x^6+22 x^5+106 x^4+58 x^3+63 x^2+75 x+2$
• $y^2=20 x^6+19 x^5+31 x^4+37 x^3+50 x^2+4 x+92$
• $y^2=71 x^6+5 x^5+43 x^4+55 x^3+99 x^2+81 x+22$
• $y^2=5 x^6+44 x^5+110 x^4+65 x^3+12 x^2+28 x+47$
• $y^2=89 x^6+7 x^5+31 x^4+94 x^3+15 x^2+94 x+3$
• $y^2=91 x^6+18 x^5+64 x^4+41 x^3+7 x^2+58 x+79$
• $y^2=18 x^6+53 x^5+46 x^4+79 x^3+104 x^2+53 x+88$
• $y^2=46 x^6+64 x^5+104 x^4+69 x^3+75 x^2+36 x+92$
• $y^2=42 x^6+66 x^5+60 x^4+56 x^3+5 x^2+109 x+92$
• $y^2=74 x^6+x^5+46 x^4+72 x^3+54 x^2+67 x+96$
• $y^2=30 x^6+14 x^5+79 x^4+10 x^3+101 x^2+38 x+77$
• $y^2=45 x^6+58 x^5+37 x^4+96 x^3+27 x^2+77 x+28$
• $y^2=110 x^6+56 x^5+23 x^4+9 x^3+101 x^2+18 x+80$
• $y^2=99 x^6+10 x^5+106 x^4+57 x^3+41 x^2+53 x+21$
• $y^2=67 x^6+42 x^5+73 x^4+46 x^3+95 x^2+102 x+22$
• $y^2=37 x^6+60 x^5+100 x^4+54 x^3+26 x^2+5 x+103$

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 4.0.2608704.1.

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.be_rb	$2$	(not in LMFDB)