Properties

Label 3.11.ar_ey_avc
Base Field $\F_{11}$
Dimension $3$
Ordinary Yes
$p$-rank $3$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{11}$
Dimension:  $3$
L-polynomial:  $( 1 - 6 x + 11 x^{2} )( 1 - 11 x + 51 x^{2} - 121 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.0215640055172$, $\pm0.140218899004$, $\pm0.270299311731$
Angle rank:  $3$ (numerical)

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

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
$A(\F_{q^r})$ 246 1350540 2306399814 3148346435040 4179274751901216 5556461382098239500 7397451961997088144126 9848654078179185243296640 13109805387201623446083283614 17449427983357018525876560000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -5 89 1303 14689 161130 1770461 19479805 214335409 2357913733 25937462824

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The isogeny class factors as 1.11.ag $\times$ 2.11.al_bz and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{11}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.11.af_ae_cm$2$(not in LMFDB)
3.11.f_ae_acm$2$(not in LMFDB)
3.11.r_ey_vc$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.11.af_ae_cm$2$(not in LMFDB)
3.11.f_ae_acm$2$(not in LMFDB)
3.11.r_ey_vc$2$(not in LMFDB)
3.11.ah_i_bg$5$(not in LMFDB)
3.11.ah_bm_afs$5$(not in LMFDB)
3.11.ac_ah_ca$5$(not in LMFDB)
3.11.d_ac_abw$5$(not in LMFDB)
3.11.ap_ec_arc$10$(not in LMFDB)
3.11.ak_bp_aeu$10$(not in LMFDB)
3.11.af_ae_cy$10$(not in LMFDB)
3.11.af_ba_aea$10$(not in LMFDB)
3.11.ad_ac_bw$10$(not in LMFDB)
3.11.c_ah_aca$10$(not in LMFDB)
3.11.f_ae_acy$10$(not in LMFDB)
3.11.f_ba_ea$10$(not in LMFDB)
3.11.h_i_abg$10$(not in LMFDB)
3.11.h_bm_fs$10$(not in LMFDB)
3.11.k_bp_eu$10$(not in LMFDB)
3.11.p_ec_rc$10$(not in LMFDB)