Properties

Label 4.5.am_cs_ake_bax
Base Field $\F_{5}$
Dimension $4$
Ordinary Yes
$p$-rank $4$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{5}$
Dimension:  $4$
L-polynomial:  $( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )^{2}$
Frobenius angles:  $\pm0.0512862249088$, $\pm0.0512862249088$, $\pm0.384619558242$, $\pm0.384619558242$
Angle rank:  $1$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

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

Point counts

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

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 49 305809 239754256 132002149041 84618786129409 57482103270113536 37328307093883814449 23386524211874297677329 14551944166392407808553744 9085114642646574814495668049

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -6 22 126 534 2754 15058 78282 392358 1953126 9755062

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
The isogeny class factors as 2.5.ag_r 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{2}, \sqrt{-3})\)$)$
Endomorphism algebra over $\overline{\F}_{5}$
The base change of $A$ to $\F_{5^{6}}$ is 1.15625.afm 4 and its endomorphism algebra is $\mathrm{M}_{4}($\(\Q(\sqrt{-6}) \)$)$
All geometric endomorphisms are defined over $\F_{5^{6}}$.
Remainder of endomorphism lattice by field

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.a_ac_a_av$2$(not in LMFDB)
4.5.m_cs_ke_bax$2$(not in LMFDB)
4.5.ag_t_abq_dg$3$(not in LMFDB)
4.5.a_ac_a_av$3$(not in LMFDB)
4.5.a_e_a_cc$3$(not in LMFDB)
4.5.g_t_bq_dg$3$(not in LMFDB)
4.5.m_cs_ke_bax$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
4.5.a_ac_a_av$2$(not in LMFDB)
4.5.m_cs_ke_bax$2$(not in LMFDB)
4.5.ag_t_abq_dg$3$(not in LMFDB)
4.5.a_ac_a_av$3$(not in LMFDB)
4.5.a_e_a_cc$3$(not in LMFDB)
4.5.g_t_bq_dg$3$(not in LMFDB)
4.5.m_cs_ke_bax$3$(not in LMFDB)
4.5.a_c_a_av$4$(not in LMFDB)
4.5.ae_i_i_abp$8$(not in LMFDB)
4.5.e_i_ai_abp$8$(not in LMFDB)
4.5.ag_p_as_q$12$(not in LMFDB)
4.5.a_ae_a_cc$12$(not in LMFDB)
4.5.a_a_a_bu$12$(not in LMFDB)
4.5.g_p_s_q$12$(not in LMFDB)
4.5.ak_bx_agk_qk$24$(not in LMFDB)
4.5.ai_bg_aea_ko$24$(not in LMFDB)
4.5.ae_g_am_bi$24$(not in LMFDB)
4.5.ae_k_abc_co$24$(not in LMFDB)
4.5.ac_b_k_acc$24$(not in LMFDB)
4.5.a_a_a_abu$24$(not in LMFDB)
4.5.c_b_ak_acc$24$(not in LMFDB)
4.5.e_g_m_bi$24$(not in LMFDB)
4.5.e_k_bc_co$24$(not in LMFDB)
4.5.i_bg_ea_ko$24$(not in LMFDB)
4.5.k_bx_gk_qk$24$(not in LMFDB)