Properties

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

Learn more about

Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $1 - 49 x + 961 x^{2} - 8869 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0989332971490$, $\pm0.164773451880$
Angle rank:  $2$ (numerical)
Number field:  \(\Q(\zeta_{5})\)
Galois group:  $C_4$
Jacobians:  11

This isogeny class is simple and geometrically 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 11 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24805 1057710005 35144116439905 1151947736663190005 37738739669628951250000 1236354708899487717310069805 40504200483258329534645066940505 1326958066935169846123396699547318405 43472473128820704835415493247002974114005 1424201691985145834249119422445933878720000000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 133 32283 5926753 1073293443 194264980098 35161843616283 6364291159308733 1151936660686152003 208500535094782804993 37738596847170094900198

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is \(\Q(\zeta_{5})\).
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.bx_bkz$2$(not in LMFDB)
2.181.ae_bu$5$(not in LMFDB)
2.181.l_ach$5$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.bx_bkz$2$(not in LMFDB)
2.181.ae_bu$5$(not in LMFDB)
2.181.l_ach$5$(not in LMFDB)
2.181.l_nx$5$(not in LMFDB)
2.181.bf_th$5$(not in LMFDB)
2.181.abf_th$10$(not in LMFDB)
2.181.al_ach$10$(not in LMFDB)
2.181.al_nx$10$(not in LMFDB)
2.181.e_bu$10$(not in LMFDB)