Properties

Label 2.625.ads_fgs
Base Field $\F_{5^{4}}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{5^{4}}$
Dimension:  $2$
L-polynomial:  $( 1 - 48 x + 625 x^{2} )^{2}$
Frobenius angles:  $\pm0.0903344706017$, $\pm0.0903344706017$
Angle rank:  $1$ (numerical)

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 a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 334084 151766343184 59594591000161156 23282963759721716121600 9094946454304799222747208964 3552713686459791604832356745353744 1387778781148779246347118189751444989316 542101086251902280142918655598654413760102400 211758236813759905613715145901175259463962656579844 82718061255306078210406331733269143812042214698857829904

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 530 388518 244099442 152587231294 95367425732690 59604644903892198 37252902994479676082 23283064365779955110014 14551915228379552598511250 9094947017729646397023063078

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
The isogeny class factors as 1.625.abw 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-1}) \)$)$
All geometric endomorphisms are defined over $\F_{5^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.625.a_aboo$2$(not in LMFDB)
2.625.ds_fgs$2$(not in LMFDB)
2.625.bw_cmp$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.625.a_aboo$2$(not in LMFDB)
2.625.ds_fgs$2$(not in LMFDB)
2.625.bw_cmp$3$(not in LMFDB)
2.625.ack_cvy$4$(not in LMFDB)
2.625.abi_wg$4$(not in LMFDB)
2.625.abc_cdq$4$(not in LMFDB)
2.625.a_boo$4$(not in LMFDB)
2.625.bc_cdq$4$(not in LMFDB)
2.625.bi_wg$4$(not in LMFDB)
2.625.ck_cvy$4$(not in LMFDB)
2.625.abw_cmp$6$(not in LMFDB)
2.625.a_azw$8$(not in LMFDB)
2.625.a_zw$8$(not in LMFDB)
2.625.ao_aqn$12$(not in LMFDB)
2.625.o_aqn$12$(not in LMFDB)