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

• Label: 2.107.abk_ur
• 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:	$( 1 - 19 x + 107 x^{2} )( 1 - 17 x + 107 x^{2} )$
	$1 - 36 x + 537 x^{2} - 3852 x^{3} + 11449 x^{4}$
Frobenius angles:	$\pm0.129482033963$, $\pm0.193011390838$
Angle rank:	$2$ (numerical)
Jacobians:	$9$
Isomorphism classes:	12

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$8099$	$128571625$	$1500467778992$	$17184295182315625$	$196719921905547219179$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$72$	$11228$	$1224828$	$131098164$	$14025858552$	$1500734378486$	$160578183332520$	$17181862022619556$	$1838459212935995556$	$196715135718433936268$

Jacobians and polarizations

This isogeny class contains the Jacobians of 9 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=34x^6+74x^5+100x^4+55x^3+10x^2+20x+79$
• $y^2=99x^6+24x^5+77x^4+13x^3+8x^2+103x+90$
• $y^2=59x^6+38x^5+87x^4+52x^3+105x^2+71x+71$
• $y^2=72x^6+28x^5+36x^4+74x^3+19x^2+22x+91$
• $y^2=72x^6+35x^5+4x^4+39x^3+33x^2+75x+50$
• $y^2=37x^6+97x^5+102x^4+61x^3+49x^2+24x+87$
• $y^2=32x^6+31x^5+14x^4+30x^3+52x^2+63x+31$
• $y^2=79x^6+40x^5+37x^4+106x^3+86x^2+25x+75$
• $y^2=59x^6+89x^5+58x^4+45x^3+38x^2+48x+106$

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{107}$

The isogeny class factors as 1.107.at $\times$ 1.107.ar and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.107.at : \(\Q(\sqrt{-67}) \).
• 1.107.ar : \(\Q(\sqrt{-139}) \).

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.ac_aef	$2$	(not in LMFDB)
2.107.c_aef	$2$	(not in LMFDB)
2.107.bk_ur	$2$	(not in LMFDB)