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

• Label: 2.107.abi_tj
• Base field: $\F_{107}$
• 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:	$\F_{107}$
Dimension:	$2$
L-polynomial:	$( 1 - 17 x + 107 x^{2} )^{2}$
	$1 - 34 x + 503 x^{2} - 3638 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.193011390838$, $\pm0.193011390838$
Angle rank:	$1$ (numerical)
Jacobians:	$21$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8281$	$129390625$	$1502065945744$	$17186390634765625$	$196721739951669013081$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$74$	$11300$	$1226132$	$131114148$	$14025988174$	$1500734660150$	$160578170506282$	$17181861725924548$	$1838459208743592524$	$196715135674201206500$

Jacobians and polarizations

This isogeny class contains the Jacobians of 21 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=58x^6+50x^5+23x^4+15x^3+23x^2+50x+58$
• $y^2=95x^6+45x^5+90x^4+76x^3+90x^2+45x+95$
• $y^2=45x^6+17x^5+45x^4+80x^3+55x^2+72x+66$
• $y^2=43x^6+50x^5+103x^4+71x^3+10x^2+23x+54$
• $y^2=82x^6+50x^5+55x^4+48x^3+62x^2+91x+36$
• $y^2=95x^6+90x^5+8x^4+32x^3+8x^2+90x+95$
• $y^2=37x^6+18x^5+54x^4+19x^3+54x^2+18x+37$
• $y^2=25x^6+103x^5+56x^4+99x^3+102x^2+77x+45$
• $y^2=10x^6+97x^5+9x^4+61x^3+9x^2+97x+10$
• $y^2=77x^6+68x^5+94x^4+6x^3+94x^2+68x+77$
• $y^2=83x^6+13x^5+79x^4+87x^3+26x^2+83x+63$
• $y^2=81x^6+101x^5+55x^4+13x^3+73x^2+106x+5$
• $y^2=70x^6+27x^5+52x^4+72x^3+97x^2+4x+87$
• $y^2=104x^6+85x^5+104x^4+58x^3+104x^2+85x+104$
• $y^2=63x^6+105x^5+95x^4+81x^3+95x^2+105x+63$
• $y^2=13x^6+51x^5+95x^4+77x^3+95x^2+51x+13$
• $y^2=35x^6+99x^5+78x^4+68x^3+78x^2+99x+35$
• $y^2=5x^6+6x^5+61x^4+50x^3+61x^2+6x+5$
• $y^2=28x^6+73x^5+81x^4+46x^3+81x^2+73x+28$
• $y^2=75x^6+11x^5+23x^4+40x^3+42x^2+34x+9$
• $y^2=103x^6+30x^5+8x^4+84x^3+63x^2+47x+55$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{107}$

The isogeny class factors as 1.107.ar^2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-139}) \)$)$

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.

Twist	Extension degree	Common base change
2.107.a_acx	$2$	(not in LMFDB)
2.107.bi_tj	$2$	(not in LMFDB)
2.107.r_ha	$3$	(not in LMFDB)