Properties

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

Invariants

 Base field: $\F_{5^{4}}$ Dimension: $2$ L-polynomial: $1 - 92 x + 3359 x^{2} - 57500 x^{3} + 390625 x^{4}$ Frobenius angles: $\pm0.0742530806974$, $\pm0.165990880443$ Angle rank: $2$ (numerical) Number field: 4.0.7219856.1 Galois group: $D_{4}$

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 a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 336393 151907341761 59598760502780676 23283052119724556073033 9094947887906422168688508393 3552713702944881815836324334845584 1387778781206832002074154197226089512297 542101086248477388847004605068707180036137353 211758236813633203058166124371156635777878191648324 82718061255303129729795447926066427326840902426866497601

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 534 388880 244116522 152587810372 95367440765094 59604645180466118 37252902996038017878 23283064365632857148932 14551915228370845665192810 9094947017729322208151469200

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.7219856.1.
All geometric endomorphisms are defined over $\F_{5^{4}}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.do_ezf $2$ (not in LMFDB)