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

• Label: 2.113.abk_vb
• 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:	$1 - 36 x + 547 x^{2} - 4068 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.121426339854$, $\pm0.222649971582$
Angle rank:	$2$ (numerical)
Number field:	4.0.13968.2
Galois group:	$D_{4}$
Jacobians:	$22$
Isomorphism classes:	22

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9213$	$160499673$	$2082265102548$	$26588175686087769$	$339463079313521825013$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$78$	$12568$	$1443114$	$163070260$	$18424695918$	$2081955073894$	$235260569766174$	$26584442001802660$	$3004041937838130666$	$339456738993126490888$

Jacobians and polarizations

This isogeny class contains the Jacobians of 22 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=101x^6+103x^5+85x^4+37x^3+97x^2+110x+61$
• $y^2=46x^6+28x^5+44x^3+76x^2+41x+39$
• $y^2=54x^6+2x^5+38x^4+57x^3+31x^2+77x+75$
• $y^2=75x^6+73x^5+46x^4+22x^3+2x^2+88x+69$
• $y^2=10x^6+18x^5+78x^4+29x^3+46x^2+56x+69$
• $y^2=43x^6+88x^5+53x^3+111x^2+97x+20$
• $y^2=41x^6+11x^5+95x^4+108x^3+89x^2+50x+54$
• $y^2=108x^6+18x^5+61x^4+67x^3+87x^2+29x+64$
• $y^2=108x^6+58x^5+65x^4+43x^3+99x^2+26x+69$
• $y^2=16x^6+101x^5+107x^4+58x^3+30x^2+26x+108$
• $y^2=20x^6+110x^5+19x^4+9x^3+83x^2+32x+88$
• $y^2=107x^6+80x^5+80x^4+54x^3+80x^2+112x+59$
• $y^2=85x^6+38x^5+x^4+27x^3+97x^2+18x+91$
• $y^2=107x^6+58x^5+27x^4+52x^3+103x^2+7x+12$
• $y^2=53x^6+82x^5+65x^4+38x^3+66x^2+38x+21$
• $y^2=96x^6+110x^5+42x^4+55x^3+x^2+43x+29$
• $y^2=61x^6+36x^5+96x^4+10x^2+53x+29$
• $y^2=15x^6+100x^5+29x^4+87x^3+x^2+37x+94$
• $y^2=73x^6+26x^5+111x^4+35x^3+80x^2+23x+55$
• $y^2=84x^6+78x^5+85x^4+42x^3+77x^2+69x+23$
• $y^2=111x^6+53x^5+84x^4+59x^3+44x^2+29x+26$
• $y^2=18x^6+11x^5+55x^4+11x^3+38x^2+63x+4$

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 4.0.13968.2.

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.bk_vb	$2$	(not in LMFDB)