Abelian variety isogeny class 1.625.aba over $\F_{5^{4}}$

• Label: 1.625.aba
• Base field: $\F_{5^{4}}$
• Dimension: $1$
• $p$-rank: $1$
• Ordinary: yes
• Supersingular: no
• Simple: yes
• Geometrically simple: yes
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: yes

Invariants

Base field:	$\F_{5^{4}}$
Dimension:	$1$
L-polynomial:	$1 - 26 x + 625 x^{2}$
Frobenius angles:	$\pm0.325931936124$
Angle rank:	$1$ (numerical)
Number field:	\(\Q(\sqrt{-114}) \)
Galois group:	$C_2$
Jacobians:	$24$
Isomorphism classes:	24

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:	$1$
Slopes:	$[0, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$600$	$391200$	$244171800$	$152588342400$	$95367423903000$

Point counts of the curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$600$	$391200$	$244171800$	$152588342400$	$95367423903000$	$59604644291853600$	$37252902976883194200$	$23283064365488038924800$	$14551915228374314750045400$	$9094947017729413243157556000$

Jacobians and polarizations

This isogeny class is principally polarizable and contains the Jacobians of 24 curves (of which 0 are hyperelliptic):

• $y^2=x^3+a^{340} x+a^{340}$
• $y^2=x^3+a^{452} x+a^{452}$
• $y^2=x^3+a^{248} x+a^{248}$
• $y^2=x^3+a^{580} x+a^{581}$
• $y^2=x^3+a^{424} x+a^{424}$
• $y^2=x^3+a^{344} x+a^{345}$
• $y^2=x^3+a^{112} x+a^{112}$
• $y^2=x^3+a^{292} x+a^{293}$
• $y^2=x^3+a^{584} x+a^{584}$
• $y^2=x^3+a^{396} x+a^{397}$
• $y^2=x^3+a^{68} x+a^{68}$
• $y^2=x^3+a^{464} x+a^{465}$
• $y^2=x^3+a^{388} x+a^{388}$
• $y^2=x^3+a^{440} x+a^{441}$
• $y^2=x^3+a^{60} x+a^{61}$
• $y^2=x^3+a^{204} x+a^{205}$
• $y^2=x^3+a^{100} x+a^{101}$
• $y^2=x^3+a^{616} x+a^{616}$
• $y^2=x^3+a^{492} x+a^{493}$
• $y^2=x^3+a^{388} x+a^{389}$
• $y^2=x^3+a^{272} x+a^{272}$
• $y^2=x^3+a^{560} x+a^{560}$
• $y^2=x^3+a^{320} x+a^{321}$
• $y^2=x^3+a^{304} x+a^{304}$

where $a$ is a root of the Conway polynomial.

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{5^{4}}$.

Endomorphism algebra over $\F_{5^{4}}$

The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-114}) \).

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
1.625.ba	$2$	(not in LMFDB)