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

• Label: 2.113.abj_uj
• 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:	$1 - 35 x + 529 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.137664879391$, $\pm0.235612203595$
Angle rank:	$2$ (numerical)
Number field:	4.0.2758925.3
Galois group:	$D_{4}$
Jacobians:	$18$
Isomorphism classes:	18

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9309$	$160943301$	$2083115228661$	$26589198285335781$	$339463767954118059264$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$79$	$12603$	$1443703$	$163076531$	$18424733294$	$2081954990907$	$235260564656063$	$26584441933772323$	$3004041937297790839$	$339456738990052731678$

Jacobians and polarizations

This isogeny class contains the Jacobians of 18 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=68x^6+4x^5+5x^4+64x^3+50x^2+111x+14$
• $y^2=63x^6+33x^5+29x^4+97x^3+41x^2+12x+67$
• $y^2=110x^6+100x^5+95x^4+56x^3+30x^2+109x+102$
• $y^2=42x^6+42x^5+104x^4+5x^3+32x^2+15x+78$
• $y^2=95x^6+9x^5+52x^4+40x^3+72x^2+11x+7$
• $y^2=58x^6+51x^5+101x^4+42x^3+36x^2+67x+55$
• $y^2=6x^6+100x^5+73x^4+74x^3+15x^2+98x+110$
• $y^2=39x^6+47x^5+68x^4+73x^3+29x^2+88x+53$
• $y^2=10x^6+24x^5+86x^4+57x^3+90x^2+84x+42$
• $y^2=14x^6+93x^5+111x^4+10x^3+87x^2+37x+18$
• $y^2=17x^6+8x^5+52x^4+51x^3+86x^2+44x+105$
• $y^2=103x^6+6x^5+5x^4+73x^3+83x^2+25x+47$
• $y^2=60x^6+87x^5+39x^4+68x^3+33x^2+61x+38$
• $y^2=39x^6+60x^5+90x^4+26x^3+67x^2+94x+111$
• $y^2=53x^6+84x^5+33x^4+70x^3+84x^2+33x+55$
• $y^2=75x^6+63x^5+71x^4+43x^3+59x^2+57x+103$
• $y^2=58x^6+99x^5+40x^4+89x^3+24x^2+108x+63$
• $y^2=24x^6+32x^5+53x^4+74x^3+64x^2+44x+25$

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 4.0.2758925.3.

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.bj_uj	$2$	(not in LMFDB)