Abelian variety isogeny class 2.107.abk_um over $\F_{107}$

• Label: 2.107.abk_um
• Base field: $\F_{107}$
• 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:	$\F_{107}$
Dimension:	$2$
L-polynomial:	$1 - 36 x + 532 x^{2} - 3852 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.0483974556481$, $\pm0.229252355639$
Angle rank:	$2$ (numerical)
Number field:	4.0.1052928.2
Galois group:	$D_{4}$
Jacobians:	$20$
Isomorphism classes:	20

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8094$	$128451780$	$1499804221662$	$17182298401952400$	$196715705773693935054$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$72$	$11218$	$1224288$	$131082934$	$14025557952$	$1500729786466$	$160578127161720$	$17181861480015646$	$1838459209216652136$	$196715135710528470418$

Jacobians and polarizations

This isogeny class contains the Jacobians of 20 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=22x^5+57x^4+86x^3+63x^2+45x+4$
• $y^2=25x^6+58x^5+90x^4+95x^3+54x^2+43x+87$
• $y^2=88x^6+45x^5+100x^4+5x^3+60x^2+77x+84$
• $y^2=66x^6+82x^5+41x^4+57x^3+106x^2+15$
• $y^2=13x^6+63x^5+88x^4+x^3+70x^2+38x+58$
• $y^2=66x^6+25x^5+49x^4+50x^3+31x^2+95x+94$
• $y^2=7x^6+49x^5+69x^4+60x^3+87x^2+104x+41$
• $y^2=93x^6+2x^5+3x^4+x^3+44x^2+83x+59$
• $y^2=105x^6+82x^5+77x^4+103x^3+26x^2+19x+63$
• $y^2=38x^6+48x^5+88x^4+19x^3+90x^2+75x+51$
• $y^2=95x^6+25x^5+81x^4+77x^3+x^2+59x+5$
• $y^2=18x^6+13x^5+51x^4+20x^3+94x^2+35x+80$
• $y^2=84x^6+89x^5+99x^4+68x^3+77x^2+15x+84$
• $y^2=32x^6+75x^5+72x^4+76x^3+8x^2+80x+19$
• $y^2=68x^6+73x^5+102x^4+85x^3+14x^2+36x+46$
• $y^2=70x^6+73x^5+28x^4+97x^3+86x^2+104x+28$
• $y^2=103x^6+29x^5+61x^4+103x^3+43x^2+42x+72$
• $y^2=96x^6+68x^5+30x^4+103x^3+27x^2+79x+81$
• $y^2=11x^6+55x^5+103x^4+22x^3+89x^2+18x+78$
• $y^2=15x^6+76x^5+46x^4+101x^3+65x^2+70x+36$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{107}$.

Endomorphism algebra over $\F_{107}$

The endomorphism algebra of this simple isogeny class is 4.0.1052928.2.

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
2.107.bk_um	$2$	(not in LMFDB)