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

• Label: 2.113.abj_ue
• 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:	$1 - 35 x + 524 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.0923236320190$, $\pm0.258475729173$
Angle rank:	$2$ (numerical)
Number field:	4.0.2395800.1
Galois group:	$D_{4}$
Jacobians:	$24$
Isomorphism classes:	24

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9304$	$160810336$	$2082355817056$	$26586920153147776$	$339459173341170922264$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$79$	$12593$	$1443178$	$163062561$	$18424483919$	$2081951780222$	$235260536314463$	$26584441832511553$	$3004041939173728714$	$339456739037700949553$

Jacobians and polarizations

This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=16x^6+88x^5+17x^4+77x^3+69x^2+20x+71$
• $y^2=64x^6+67x^5+110x^4+15x^3+94x^2+88x+23$
• $y^2=76x^6+7x^5+12x^4+63x^3+13x^2+70x+50$
• $y^2=37x^6+39x^5+18x^4+22x^3+23x^2+108x+87$
• $y^2=37x^6+5x^5+33x^4+44x^3+112x^2+53x+52$
• $y^2=88x^6+70x^5+18x^4+73x^3+48x^2+48x+54$
• $y^2=29x^6+66x^5+63x^4+61x^3+57x^2+4x+45$
• $y^2=19x^6+x^5+85x^4+104x^3+14x^2+30x+99$
• $y^2=84x^6+64x^5+13x^4+28x^3+106x^2+17x+6$
• $y^2=54x^6+7x^5+40x^4+99x^3+87x^2+38x+8$
• $y^2=76x^6+84x^5+2x^4+16x^3+59x^2+75x+103$
• $y^2=50x^6+92x^5+100x^4+69x^3+20x^2+75x+95$
• $y^2=53x^6+92x^5+76x^4+87x^3+97x^2+17x+80$
• $y^2=70x^6+11x^5+33x^3+28x^2+20x+111$
• $y^2=55x^6+109x^5+49x^4+70x^3+68x^2+26x+98$
• $y^2=96x^6+3x^5+36x^4+x^3+25x^2+102x+107$
• $y^2=73x^6+43x^5+20x^4+22x^3+109x^2+13x+29$
• $y^2=x^6+87x^5+36x^4+22x^3+73x^2+95x+29$
• $y^2=34x^6+90x^5+32x^4+93x^3+46x^2+75x+16$
• $y^2=101x^6+9x^5+71x^4+75x^3+109x^2+58x+9$
• $y^2=42x^6+11x^5+67x^4+106x^3+98x^2+48x+34$
• $y^2=93x^6+23x^5+75x^4+88x^3+39x^2+102x+52$
• $y^2=55x^6+22x^5+36x^4+72x^3+65x^2+99x+23$
• $y^2=88x^6+x^5+88x^4+41x^3+103x^2+72x+26$

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 4.0.2395800.1.

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_ue	$2$	(not in LMFDB)