Abelian variety isogeny class 2.173.abv_bih over $\F_{173}$

• Label: 2.173.abv_bih
• Base field: $\F_{173}$
• 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:	$\F_{173}$
Dimension:	$2$
L-polynomial:	$1 - 47 x + 891 x^{2} - 8131 x^{3} + 29929 x^{4}$
Frobenius angles:	$\pm0.0295549099493$, $\pm0.209571521819$
Angle rank:	$2$ (numerical)
Number field:	4.0.1295981.1
Galois group:	$D_{4}$
Jacobians:	$4$

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$22643$	$883054357$	$26795371452119$	$802356061053561989$	$24013819389124717592848$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$127$	$29503$	$5175133$	$895741563$	$154963966542$	$26808751691983$	$4637914232111917$	$802359176212931091$	$138808137838487926399$	$24013807852129267532118$

Jacobians and polarizations

This isogeny class contains the Jacobians of 4 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=86x^6+158x^5+3x^4+8x^3+98x^2+108x+57$
• $y^2=60x^6+95x^5+36x^4+131x^3+63x^2+19x+111$
• $y^2=87x^6+38x^5+164x^4+112x^3+138x^2+9x+71$
• $y^2=103x^6+57x^5+131x^4+112x^3+142x^2+17x+3$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{173}$.

Endomorphism algebra over $\F_{173}$

The endomorphism algebra of this simple isogeny class is 4.0.1295981.1.

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
2.173.bv_bih	$2$	(not in LMFDB)