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

• Label: 2.113.abj_ub
• 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:	$1 - 35 x + 521 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0623216346094$, $\pm0.268275041768$
Angle rank:	$2$ (numerical)
Number field:	4.0.107725.1
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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9301$	$160730581$	$2081900207869$	$26585545472686981$	$339456339200985339136$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$79$	$12587$	$1442863$	$163054131$	$18424330094$	$2081949664763$	$235260513494183$	$26584441635303523$	$3004041937723173559$	$339456739026145333022$

Jacobians and polarizations

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

• $y^2=43x^6+55x^5+87x^4+38x^3+20x^2+2x+16$
• $y^2=98x^6+65x^5+96x^4+104x^3+24x^2+6x+75$
• $y^2=70x^6+49x^5+23x^4+16x^3+109x^2+21x+24$
• $y^2=45x^6+16x^5+69x^4+101x^3+101x^2+24x+58$
• $y^2=93x^6+10x^5+13x^4+15x^3+86x^2+2x+54$
• $y^2=28x^6+6x^5+72x^4+20x^3+38x^2+71x+91$
• $y^2=39x^6+61x^5+76x^4+17x^3+92x^2+44x+112$
• $y^2=45x^6+86x^5+91x^4+34x^3+31x^2+67x+63$
• $y^2=10x^6+49x^5+29x^4+7x^3+3x^2+19x+35$
• $y^2=69x^6+23x^5+40x^4+71x^3+20x^2+85x+20$
• $y^2=49x^6+2x^5+40x^4+80x^3+53x^2+30x+94$
• $y^2=107x^6+3x^5+24x^4+21x^3+9x^2+51x+104$
• $y^2=45x^6+26x^5+59x^4+28x^3+71x^2+33x+44$
• $y^2=108x^6+98x^5+79x^4+87x^3+16x^2+16x+11$
• $y^2=37x^6+58x^5+23x^4+92x^3+13x^2+45x+43$
• $y^2=12x^6+29x^5+74x^4+13x^3+99x^2+109x+42$
• $y^2=73x^6+111x^5+90x^4+4x^3+33x^2+54x+75$
• $y^2=76x^6+21x^5+69x^4+112x^3+19x^2+108x+34$

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 4.0.107725.1.

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.bj_ub	$2$	(not in LMFDB)