# Properties

 Label 2.625.adw_fog Base Field $\F_{5^{4}}$ Dimension $2$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

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

This isogeny class is not simple.

## Newton polygon

This isogeny class is supersingular.

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

## Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 331776 151613669376 59589387451109376 23282825947723387109376 9094943292439556121787109376 3552713620592840373516081787109376 1387778779871950973980128765081787109376 542101086228541362288664095103740081787109376 211758236813353040162155681173317134365081787109376 82718061255299298040188915647377143613993740081787109376

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 526 388126 244078126 152586328126 95367392578126 59604643798828126 37252902960205078126 23283064364776611328126 14551915228351593017578126 9094947017728900909423828126

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The isogeny class factors as 1.625.aby 2 and its endomorphism algebra is $\mathrm{M}_{2}(B)$, where $B$ is the quaternion algebra over $$\Q$$ ramified at $5$ and $\infty$.
All geometric endomorphisms are defined over $\F_{5^{4}}$.

## Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{5^{4}}$.

 Subfield Primitive Model $\F_{5}$ 2.5.a_ak $\F_{5}$ 2.5.a_k

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.a_abwc $2$ (not in LMFDB) 2.625.dw_fog $2$ (not in LMFDB) 2.625.az_a $3$ (not in LMFDB) 2.625.by_cud $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.625.a_abwc $2$ (not in LMFDB) 2.625.dw_fog $2$ (not in LMFDB) 2.625.az_a $3$ (not in LMFDB) 2.625.by_cud $3$ (not in LMFDB) 2.625.a_bwc $4$ (not in LMFDB) 2.625.z_yb $5$ (not in LMFDB) 2.625.acx_dse $6$ (not in LMFDB) 2.625.aby_cud $6$ (not in LMFDB) 2.625.a_yb $6$ (not in LMFDB) 2.625.z_a $6$ (not in LMFDB) 2.625.cx_dse $6$ (not in LMFDB) 2.625.a_a $8$ (not in LMFDB) 2.625.az_yb $10$ (not in LMFDB) 2.625.a_ayb $12$ (not in LMFDB)