Abelian variety isogeny class 4.5.am_cw_alc_bdr over $\F_{5}$

• Label: 4.5.am_cw_alc_bdr
• Base field: $\F_{5}$
• Dimension: $4$
• $p$-rank: $4$
• Ordinary: yes
• Supersingular: no
• Simple: no
• Geometrically simple: no
• Primitive: yes
• Principally polarizable: yes
• Contains a Jacobian: no

Invariants

Base field:	$\F_{5}$
Dimension:	$4$
L-polynomial:	$( 1 - 3 x + 5 x^{2} )^{4}$
	$1 - 12 x + 74 x^{2} - 288 x^{3} + 771 x^{4} - 1440 x^{5} + 1850 x^{6} - 1500 x^{7} + 625 x^{8}$
Frobenius angles:	$\pm0.265942140215$, $\pm0.265942140215$, $\pm0.265942140215$, $\pm0.265942140215$
Angle rank:	$1$ (numerical)

This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable.

Newton polygon

This isogeny class is ordinary.

$p$-rank:	$4$
Slopes:	$[0, 0, 0, 0, 1, 1, 1, 1]$

Point counts

Point counts of the abelian variety

$r$	$1$	$2$	$3$	$4$	$5$
$A(\F_{q^r})$	$81$	$531441$	$429981696$	$207594140625$	$102647069357121$

Point counts of the (virtual) curve

$r$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$C(\F_{q^r})$	$-6$	$30$	$198$	$822$	$3354$	$15330$	$76098$	$386022$	$1949454$	$9777630$

Jacobians and polarizations

This isogeny class is principally polarizable, but does not contain a Jacobian.

Decomposition and endomorphism algebra

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

Endomorphism algebra over $\F_{5}$

The isogeny class factors as 1.5.ad^4 and its endomorphism algebra is $\mathrm{M}_{4}($\(\Q(\sqrt{-11}) \)$)$

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
4.5.ag_u_abk_cr	$2$	(not in LMFDB)
4.5.a_c_a_bz	$2$	(not in LMFDB)
4.5.g_u_bk_cr	$2$	(not in LMFDB)
4.5.m_cw_lc_bdr	$2$	(not in LMFDB)
4.5.ad_f_s_acc	$3$	(not in LMFDB)
4.5.g_r_cc_ga	$3$	(not in LMFDB)