Abelian variety isogeny class 2.103.abh_rz over $\F_{103}$

• Label: 2.103.abh_rz
• Base field: $\F_{103}$
• 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:	$\F_{103}$
Dimension:	$2$
L-polynomial:	$1 - 33 x + 467 x^{2} - 3399 x^{3} + 10609 x^{4}$
Frobenius angles:	$\pm0.0666761623751$, $\pm0.275751116212$
Angle rank:	$2$ (numerical)
Number field:	4.0.106525.1
Galois group:	$D_{4}$
Jacobians:	$27$
Isomorphism classes:	27

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7645$	$110921305$	$1194159634195$	$12668367167178525$	$134391318128448898000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$71$	$10455$	$1092827$	$112556803$	$11592713156$	$1194050601915$	$122987362578977$	$12667700657878003$	$1304773184404949681$	$134391637962787797150$

Jacobians and polarizations

This isogeny class contains the Jacobians of 27 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=15x^6+80x^5+29x^4+9x^3+4x^2+60x+101$
• $y^2=91x^6+56x^5+58x^4+85x^3+96x^2+30x+91$
• $y^2=54x^6+21x^5+34x^4+63x^3+58x^2+57x+6$
• $y^2=40x^6+46x^5+98x^4+90x^3+3x^2+31x+10$
• $y^2=72x^6+11x^5+47x^4+9x^3+67x^2+58x+12$
• $y^2=36x^6+72x^5+73x^4+72x^3+20x^2+26x+42$
• $y^2=21x^6+40x^5+13x^4+69x^3+15x^2+43x+18$
• $y^2=22x^6+33x^5+90x^4+77x^3+25x^2+45x+10$
• $y^2=81x^6+48x^5+45x^4+11x^3+55x^2+67x+59$
• $y^2=75x^6+89x^4+39x^3+77x^2+89x+17$
• $y^2=22x^6+90x^5+55x^4+48x^3+16x^2+96x+36$
• $y^2=2x^6+18x^5+100x^4+81x^3+9x^2+44x+7$
• $y^2=20x^6+41x^5+98x^4+45x^3+59x^2+102x+28$
• $y^2=22x^6+75x^5+28x^4+23x^3+11x^2+39x+94$
• $y^2=46x^6+55x^5+27x^4+69x^3+25x^2+52x+65$
• $y^2=53x^6+81x^5+11x^4+26x^3+78x^2+94x+75$
• $y^2=74x^6+16x^5+50x^4+92x^3+97x^2+41x+86$
• $y^2=20x^6+53x^5+94x^4+86x^3+59x^2+30x+69$
• $y^2=78x^6+73x^5+75x^4+51x^3+5x^2+5x+4$
• $y^2=96x^6+68x^5+33x^4+70x^3+84x^2+58x+51$
• $y^2=94x^6+5x^5+38x^4+37x^3+62x^2+66x+80$
• $y^2=65x^6+46x^5+64x^4+70x^3+14x^2+51x+37$
• $y^2=100x^6+81x^5+8x^4+2x^3+102x^2+52x+13$
• $y^2=43x^6+36x^5+48x^4+27x^3+76x^2+x+46$
• $y^2=45x^6+57x^5+7x^4+39x^3+20x^2+77x+4$
• $y^2=4x^6+12x^5+18x^4+19x^3+62x^2+95x+11$
• $y^2=x^6+83x^5+12x^4+39x^3+66x^2+59x+26$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{103}$.

Endomorphism algebra over $\F_{103}$

The endomorphism algebra of this simple isogeny class is 4.0.106525.1.

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
2.103.bh_rz	$2$	(not in LMFDB)