Properties

 Label 2.19.am_cv Base Field $\F_{19}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{19}$ Dimension: $2$ L-polynomial: $( 1 - 7 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$ Frobenius angles: $\pm0.203259864187$, $\pm0.305569972467$ Angle rank: $2$ (numerical) Jacobians: 8

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 contains the Jacobians of 8 curves, and hence is principally polarizable:

• $y^2=3x^6+7x^5+7x+3$
• $y^2=8x^6+9x^5+13x^4+4x^3+12x^2+17x+12$
• $y^2=16x^6+x^5+10x^4+17x^3+18x^2+4x+5$
• $y^2=13x^6+9x^5+13x^4+7x^3+12x^2+17x+10$
• $y^2=14x^6+x^5+2x^4+15x^3+13x^2+9x+2$
• $y^2=3x^6+17x^5+x^4+10x^3+x^2+17x+3$
• $y^2=10x^6+8x^5+8x^4+18x^3+12x^2+18x+10$
• $y^2=13x^6+15x^5+7x^4+2x^3+7x^2+15x+13$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 195 131625 48550320 17134547625 6138171800475 2213253727776000 798971085669032835 288438938659422383625 104127294467636946782640 37589973152955087548165625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 8 364 7076 131476 2478968 47044582 893831912 16983417316 322687524764 6131066208124

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{19}$
 The isogeny class factors as 1.19.ah $\times$ 1.19.af 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.ac_d $2$ (not in LMFDB) 2.19.c_d $2$ (not in LMFDB) 2.19.m_cv $2$ (not in LMFDB) 2.19.ag_br $3$ (not in LMFDB) 2.19.d_ac $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.19.ac_d $2$ (not in LMFDB) 2.19.c_d $2$ (not in LMFDB) 2.19.m_cv $2$ (not in LMFDB) 2.19.ag_br $3$ (not in LMFDB) 2.19.d_ac $3$ (not in LMFDB) 2.19.an_da $6$ (not in LMFDB) 2.19.ae_bh $6$ (not in LMFDB) 2.19.ad_ac $6$ (not in LMFDB) 2.19.e_bh $6$ (not in LMFDB) 2.19.g_br $6$ (not in LMFDB) 2.19.n_da $6$ (not in LMFDB)