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

Learn more about

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.

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

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