# Properties

 Label 2.625.adp_fay 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: $1 - 93 x + 3404 x^{2} - 58125 x^{3} + 390625 x^{4}$ Frobenius angles: $\pm0.0504914747344$, $\pm0.162461973402$ Angle rank: $2$ (numerical) Number field: 4.0.10132056.2 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 $A(\F_{q^r})$ 335812 151870305376 59597561313658624 23283022426840033895808 9094947258961836567512982532 3552713690925025742425014646841344 1387778780992520692511845470737038473028 542101086244822113288969272127315005757838848 211758236813572410271651503459764619979749293821696 82718061255302132335600696260157150249487961486466612576

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 533 388785 244111610 152587615777 95367434170133 59604644978806398 37252902990285142469 23283064365475864259137 14551915228366668016714202 9094947017729212543500008625

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5^{4}}$
 The endomorphism algebra of this simple isogeny class is 4.0.10132056.2.
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.dp_fay $2$ (not in LMFDB)