Abelian variety isogeny class 2.97.abi_sn over $\F_{97}$

• Label: 2.97.abi_sn
• Base field: $\F_{97}$
• 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:	$\F_{97}$
Dimension:	$2$
L-polynomial:	$1 - 34 x + 481 x^{2} - 3298 x^{3} + 9409 x^{4}$
Frobenius angles:	$\pm0.115542665113$, $\pm0.209431487650$
Angle rank:	$2$ (numerical)
Number field:	4.0.454208.1
Galois group:	$D_{4}$
Jacobians:	$6$
Isomorphism classes:	6

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$6559$	$86729657$	$832849043068$	$7838690319417209$	$73744371538716558799$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$64$	$9216$	$912538$	$88543476$	$8587568364$	$832974310038$	$80798301224236$	$7837433673730404$	$760231058753694394$	$73742412688234161616$

Jacobians and polarizations

This isogeny class contains the Jacobians of 6 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=94x^6+9x^5+22x^4+39x^3+65x^2+12x+33$
• $y^2=92x^6+63x^5+86x^4+23x^3+28x^2+57x+24$
• $y^2=45x^6+78x^5+96x^4+41x^3+76x^2+33x+60$
• $y^2=54x^6+82x^5+38x^4+30x^3+78x^2+5x+64$
• $y^2=67x^6+62x^5+36x^4+19x^3+9x^2+55x+39$
• $y^2=95x^6+27x^5+14x^4+38x^3+69x^2+30x+41$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{97}$.

Endomorphism algebra over $\F_{97}$

The endomorphism algebra of this simple isogeny class is 4.0.454208.1.

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
2.97.bi_sn	$2$	(not in LMFDB)