# Properties

 Label 4.5.al_ce_aha_ri Base Field $\F_{5}$ Dimension $4$ Ordinary No $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{5}$ Dimension: $4$ L-polynomial: $( 1 - 4 x + 5 x^{2} )( 1 - 7 x + 23 x^{2} - 55 x^{3} + 115 x^{4} - 175 x^{5} + 125 x^{6} )$ Frobenius angles: $\pm0.0441569735346$, $\pm0.147583617650$, $\pm0.210407616474$, $\pm0.568817170463$ Angle rank: $4$ (numerical)

This isogeny class is not simple.

## Newton polygon

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1/2, 1/2, 1, 1, 1]$

## 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 $A(\F_{q^r})$ 54 270540 195495606 148498323840 101585855236734 60772837352036940 37124083642174038144 23284050299033598973440 14555721144181616923404438 9085575765610606761485642700

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -5 17 97 609 3325 15929 77856 390641 1953637 9755557

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{5}$
 The isogeny class factors as 1.5.ae $\times$ 3.5.ah_x_acd and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{5}$.

## 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 4.5.ad_a_c_k $2$ (not in LMFDB) 4.5.d_a_ac_k $2$ (not in LMFDB) 4.5.l_ce_ha_ri $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 4.5.ad_a_c_k $2$ (not in LMFDB) 4.5.d_a_ac_k $2$ (not in LMFDB) 4.5.l_ce_ha_ri $2$ (not in LMFDB) 4.5.aj_bq_afg_nc $4$ (not in LMFDB) 4.5.af_o_abs_eq $4$ (not in LMFDB) 4.5.f_o_bs_eq $4$ (not in LMFDB) 4.5.j_bq_fg_nc $4$ (not in LMFDB)