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

• Label: 2.103.abj_tq
• Base field: $\F_{103}$
• Dimension: $2$
• $p$-rank: $2$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{103}$
Dimension:	$2$
L-polynomial:	$( 1 - 19 x + 103 x^{2} )( 1 - 16 x + 103 x^{2} )$
	$1 - 35 x + 510 x^{2} - 3605 x^{3} + 10609 x^{4}$
Frobenius angles:	$\pm0.114441478345$, $\pm0.210980441649$
Angle rank:	$2$ (numerical)
Jacobians:	$24$
Isomorphism classes:	80

This isogeny class is not 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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$7480$	$110404800$	$1193900662240$	$12669491783520000$	$134394658746291387400$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$69$	$10405$	$1092588$	$112566793$	$11593001319$	$1194054972190$	$122987406141753$	$12667700905836913$	$1304773183933559844$	$134391637933432516525$

Jacobians and polarizations

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

• $y^2=88x^6+19x^5+61x^4+13x^3+64x^2+25x+47$
• $y^2=97x^6+45x^5+62x^4+44x^3+56x^2+50x+39$
• $y^2=40x^6+50x^5+44x^4+21x^3+62x^2+74x+3$
• $y^2=29x^6+77x^5+81x^4+71x^3+2x^2+13x+96$
• $y^2=62x^5+99x^3+80x^2+81x+18$
• $y^2=30x^6+78x^5+87x^4+2x^3+42x^2+8x+6$
• $y^2=39x^6+91x^5+78x^4+22x^3+64x^2+28x+57$
• $y^2=19x^6+44x^5+90x^4+35x^3+67x^2+74x+15$
• $y^2=31x^6+94x^5+51x^4+67x^3+51x^2+41x+52$
• $y^2=43x^6+78x^5+13x^4+96x^3+49x^2+39x+47$
• $y^2=82x^6+3x^5+24x^4+13x^3+57x^2+12x+5$
• $y^2=75x^6+73x^5+47x^4+14x^3+88x^2+20x+70$
• $y^2=38x^6+85x^5+101x^4+17x^3+27x^2+40x+97$
• $y^2=100x^6+35x^5+11x^4+76x^3+92x^2+57x+39$
• $y^2=95x^6+54x^5+36x^4+39x^3+64x^2+10x+62$
• $y^2=67x^6+6x^5+10x^4+88x^3+26x^2+15x+24$
• $y^2=35x^6+94x^5+15x^4+38x^3+68x^2+80x+49$
• $y^2=101x^6+37x^5+81x^4+21x^3+81x^2+65x+97$
• $y^2=50x^6+99x^5+101x^4+64x^3+95x^2+15x+59$
• $y^2=102x^6+24x^5+40x^4+81x^3+17x^2+99x+48$
• $y^2=6x^6+3x^5+x^4+34x^3+41x^2+58x+47$
• $y^2=10x^6+43x^5+96x^4+95x^3+5x^2+94x+60$
• $y^2=32x^6+73x^5+78x^4+71x^3+73x^2+89x+31$
• $y^2=16x^6+82x^5+38x^4+100x^3+80x^2+32x+92$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{103}$

The isogeny class factors as 1.103.at $\times$ 1.103.aq and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.103.at : \(\Q(\sqrt{-51}) \).
• 1.103.aq : \(\Q(\sqrt{-39}) \).

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.ad_adu	$2$	(not in LMFDB)
2.103.d_adu	$2$	(not in LMFDB)
2.103.bj_tq	$2$	(not in LMFDB)