Properties

 Label 2.625.adv_fmi Base Field $\F_{5^{4}}$ Dimension $2$ Ordinary No $p$-rank $1$ Principally polarizable Yes Contains a Jacobian No

Invariants

 Base field: $\F_{5^{4}}$ Dimension: $2$ L-polynomial: $( 1 - 25 x )^{2}( 1 - 49 x + 625 x^{2} )$ Frobenius angles: $0$, $0$, $\pm0.0637685608585$ Angle rank: $1$ (numerical)

This isogeny class is not simple.

Newton polygon

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 332352 151652217600 59590724194052352 23282862217526698675200 9094944151318564946239474752 3552713639205190684910894599372800 1387778780250456799889751804783109657152 542101086235873289430185046325370798302310400 211758236813489612674032135393014923177567564599552 82718061255301759941029364420712619518542369687883488000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 527 388225 244083602 152586565825 95367401584127 59604644111091550 37252902970365516527 23283064365091515201025 14551915228360978209130802 9094947017729171598283878625

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The isogeny class factors as 1.625.aby $\times$ 1.625.abx and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: 1.625.aby : the quaternion algebra over $$\Q$$ ramified at $5$ and $\infty$. 1.625.abx : $$\Q(\sqrt{-11})$$.
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.ab_abue $2$ (not in LMFDB) 2.625.b_abue $2$ (not in LMFDB) 2.625.dv_fmi $2$ (not in LMFDB) 2.625.ay_z $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.ab_abue $2$ (not in LMFDB) 2.625.b_abue $2$ (not in LMFDB) 2.625.dv_fmi $2$ (not in LMFDB) 2.625.ay_z $3$ (not in LMFDB) 2.625.acw_drf $6$ (not in LMFDB) 2.625.y_z $6$ (not in LMFDB) 2.625.cw_drf $6$ (not in LMFDB)