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

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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 246 1350540 2306399814 3148346435040 4179274751901216 5556461382098239500 7397451961997088144126 9848654078179185243296640 13109805387201623446083283614 17449427983357018525876560000000

 $r$ 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.
 Twist Extension Degree Common 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.
 Twist Extension Degree Common 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)