Abelian variety isogeny class 2.73.aba_ln over $\F_{73}$

• Label: 2.73.aba_ln
• Base field: $\F_{73}$
• 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:	$\F_{73}$
Dimension:	$2$
L-polynomial:	$( 1 - 17 x + 73 x^{2} )( 1 - 9 x + 73 x^{2} )$
	$1 - 26 x + 299 x^{2} - 1898 x^{3} + 5329 x^{4}$
Frobenius angles:	$\pm0.0323195869136$, $\pm0.323434683416$
Angle rank:	$2$ (numerical)
Jacobians:	$12$
Isomorphism classes:	36

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

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$3705$	$27983865$	$151353755280$	$806364724408425$	$4297392935156060025$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$48$	$5252$	$389070$	$28394884$	$2072959248$	$151332823694$	$11047388992464$	$806460068239876$	$58871586878286750$	$4297625830589537732$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

• $y^2=26x^6+48x^5+66x^4+31x^3+x^2+48x+14$
• $y^2=15x^6+20x^5+23x^4+41x^3+25x^2+5x+62$
• $y^2=17x^6+5x^5+54x^4+58x^3+35x^2+41x+53$
• $y^2=29x^6+48x^5+8x^4+19x^3+4x^2+12x+31$
• $y^2=16x^6+55x^5+61x^4+29x^3+67x^2+32x+2$
• $y^2=16x^6+66x^5+44x^4+37x^3+34x^2+9x+28$
• $y^2=33x^6+53x^5+50x^4+28x^3+45x^2+18x+42$
• $y^2=40x^6+54x^5+67x^4+69x^3+57x^2+54x+10$
• $y^2=40x^6+2x^5+66x^4+17x^3+66x^2+26x+59$
• $y^2=17x^6+27x^5+30x^4+72x^3+60x^2+27x+42$
• $y^2=8x^6+11x^5+65x^4+17x^3+5x^2+63x+60$
• $y^2=18x^6+55x^5+16x^4+6x^3+40x^2+37x+39$

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{73}$.

Endomorphism algebra over $\F_{73}$

The isogeny class factors as 1.73.ar $\times$ 1.73.aj and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:

• 1.73.ar : \(\Q(\sqrt{-3}) \).
• 1.73.aj : \(\Q(\sqrt{-211}) \).

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
2.73.ai_ah	$2$	(not in LMFDB)
2.73.i_ah	$2$	(not in LMFDB)
2.73.ba_ln	$2$	(not in LMFDB)
2.73.ac_df	$3$	(not in LMFDB)
2.73.b_ce	$3$	(not in LMFDB)