# Properties

 Label 2.19.an_dc Base Field $\F_{19}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{19}$ Dimension: $2$ L-polynomial: $( 1 - 7 x + 19 x^{2} )( 1 - 6 x + 19 x^{2} )$ Frobenius angles: $\pm0.203259864187$, $\pm0.258380448083$ Angle rank: $2$ (numerical) Jacobians: 0

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

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

## 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 $A(\F_{q^r})$ 182 127764 48315176 17156149920 6143598863402 2213711304831936 798975439788211322 288435376972587761280 104126843995038193192136 37589951156111042988102804

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 7 353 7042 131641 2481157 47054306 893836783 16983207601 322686128758 6131062620353

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{19}$
 The isogeny class factors as 1.19.ah $\times$ 1.19.ag 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 $\F_{19}$.

## 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 2.19.ab_ae $2$ (not in LMFDB) 2.19.b_ae $2$ (not in LMFDB) 2.19.n_dc $2$ (not in LMFDB) 2.19.ah_bs $3$ (not in LMFDB) 2.19.c_ak $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.19.ab_ae $2$ (not in LMFDB) 2.19.b_ae $2$ (not in LMFDB) 2.19.n_dc $2$ (not in LMFDB) 2.19.ah_bs $3$ (not in LMFDB) 2.19.c_ak $3$ (not in LMFDB) 2.19.ao_di $6$ (not in LMFDB) 2.19.af_bg $6$ (not in LMFDB) 2.19.ac_ak $6$ (not in LMFDB) 2.19.f_bg $6$ (not in LMFDB) 2.19.h_bs $6$ (not in LMFDB) 2.19.o_di $6$ (not in LMFDB)