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

• Label: 2.113.abj_uh
• 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:	$1 - 35 x + 527 x^{2} - 3955 x^{3} + 12769 x^{4}$
Frobenius angles:	$\pm0.119021368587$, $\pm0.246263793614$
Angle rank:	$2$ (numerical)
Number field:	4.0.5869269.1
Galois group:	$D_{4}$
Jacobians:	$8$
Isomorphism classes:	8

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$9307$	$160890109$	$2082811454539$	$26588288982671941$	$339461949451971424432$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$79$	$12599$	$1443493$	$163070955$	$18424634594$	$2081953753823$	$235260554764433$	$26584441926826579$	$3004041938668434379$	$339456739018370007614$

Jacobians and polarizations

This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=20x^6+112x^5+100x^4+11x^3+50x^2+71x+18$
• $y^2=90x^6+87x^5+77x^4+22x^3+110x^2+72x+32$
• $y^2=33x^6+62x^5+41x^4+25x^3+47x^2+21x+71$
• $y^2=39x^6+44x^5+44x^4+43x^3+30x^2+72x+33$
• $y^2=17x^6+101x^5+71x^4+94x^3+79x^2+31x+51$
• $y^2=14x^6+42x^5+107x^4+19x^3+103x^2+91x+37$
• $y^2=54x^6+95x^5+89x^4+74x^3+2x^2+105x+96$
• $y^2=29x^6+97x^5+97x^4+47x^3+92x^2+58x+27$

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 4.0.5869269.1.

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_uh	$2$	(not in LMFDB)