# Properties

 Label 2.625.adq_fct 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: $1 - 94 x + 3451 x^{2} - 58750 x^{3} + 390625 x^{4}$ Frobenius angles: $\pm0.0263772007358$, $\pm0.155227168270$ Angle rank: $2$ (numerical) Number field: 4.0.601664.1 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 $A(\F_{q^r})$ 335233 151834065593 59596429545179200 23282995845275515592873 9094946733365078666128682353 3552713681650338862283693853516800 1387778780839107685155321767863812531313 542101086242303558062080156330817409983315913 211758236813528820357712888888550378256790187252800 82718061255301311464087921680783956125262427956573422553

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 532 388692 244106974 152587441572 95367428658852 59604644823202974 37252902986166993412 23283064365367693135812 14551915228363672540637374 9094947017729122287722688052

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.601664.1.
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.dq_fct $2$ (not in LMFDB)