Properties

Label 2.181.aca_bny
Base Field $\F_{181}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $( 1 - 26 x + 181 x^{2} )^{2}$
Frobenius angles:  $\pm0.0828936782352$, $\pm0.0828936782352$
Angle rank:  $1$ (numerical)
Jacobians:  8

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24336 1052872704 35120842048656 1151865665532002304 37738505921630646287376 1236354164391636545149440000 40504199512701896227619649361296 1326958066062810715140931778289598464 43472473131239557380299012767952375947536 1424201692002246333765865470710586879106781184

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 130 32134 5922826 1073216974 194263776850 35161828130518 6364291006808410 1151936659928854174 208500535106383986466 37738596847623225142054

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.aba 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-3}) \)$)$
All geometric endomorphisms are defined over $\F_{181}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.a_amc$2$(not in LMFDB)
2.181.ca_bny$2$(not in LMFDB)
2.181.at_gy$3$(not in LMFDB)
2.181.ah_afc$3$(not in LMFDB)
2.181.o_pv$3$(not in LMFDB)
2.181.ba_tb$3$(not in LMFDB)
2.181.bm_bbv$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.a_amc$2$(not in LMFDB)
2.181.ca_bny$2$(not in LMFDB)
2.181.at_gy$3$(not in LMFDB)
2.181.ah_afc$3$(not in LMFDB)
2.181.o_pv$3$(not in LMFDB)
2.181.ba_tb$3$(not in LMFDB)
2.181.bm_bbv$3$(not in LMFDB)
2.181.a_mc$4$(not in LMFDB)
2.181.abt_bgy$6$(not in LMFDB)
2.181.abm_bbv$6$(not in LMFDB)
2.181.abh_uy$6$(not in LMFDB)
2.181.aba_tb$6$(not in LMFDB)
2.181.ao_pv$6$(not in LMFDB)
2.181.am_iv$6$(not in LMFDB)
2.181.a_b$6$(not in LMFDB)
2.181.a_mb$6$(not in LMFDB)
2.181.h_afc$6$(not in LMFDB)
2.181.m_iv$6$(not in LMFDB)
2.181.t_gy$6$(not in LMFDB)
2.181.bh_uy$6$(not in LMFDB)
2.181.bt_bgy$6$(not in LMFDB)
2.181.a_amb$12$(not in LMFDB)
2.181.a_ab$12$(not in LMFDB)