Properties

 Label 2.139.abp_baq Base Field $\F_{139}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{139}$ Dimension: $2$ L-polynomial: $( 1 - 23 x + 139 x^{2} )( 1 - 18 x + 139 x^{2} )$ Frobenius angles: $\pm0.0707251543800$, $\pm0.223543330897$ 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:

• $y^2=85x^6+123x^5+99x^4+110x^3+83x^2+58x+7$
• $y^2=3x^6+87x^5+101x^4+35x^3+75x^2+71x+108$
• $y^2=38x^6+75x^5+118x^4+80x^3+70x^2+4x+57$
• $y^2=132x^6+126x^5+122x^4+94x^3+120x^2+5x+13$
• $y^2=29x^6+122x^5+31x^4+132x^3+x^2+123x+136$
• $y^2=105x^6+19x^5+51x^4+8x^3+118x^2+15x+29$
• $y^2=99x^6+8x^5+11x^4+6x^3+14x^2+49x+59$
• $y^2=17x^6+102x^5+120x^4+122x^3+74x^2+38x+52$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14274 367612596 7210128042936 139358209022326944 2692463754100883071374 52020878445522817743197376 1005095196851466588777575558334 19419444504822634411935927814360704 375203088347549871681192507667165304856 7249298871847897532620977595416190369279476

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 99 19025 2684718 373313209 51889067289 7212550717586 1002544354646451 139353666777378289 19370159737288567722 2692452204183174022625

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
 The isogeny class factors as 1.139.ax $\times$ 1.139.as 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 $\F_{139}$.

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 2.139.af_afg $2$ (not in LMFDB) 2.139.f_afg $2$ (not in LMFDB) 2.139.bp_baq $2$ (not in LMFDB) 2.139.al_fw $3$ (not in LMFDB) 2.139.ac_ak $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.139.af_afg $2$ (not in LMFDB) 2.139.f_afg $2$ (not in LMFDB) 2.139.bp_baq $2$ (not in LMFDB) 2.139.al_fw $3$ (not in LMFDB) 2.139.ac_ak $3$ (not in LMFDB) 2.139.abi_vu $6$ (not in LMFDB) 2.139.az_po $6$ (not in LMFDB) 2.139.c_ak $6$ (not in LMFDB) 2.139.l_fw $6$ (not in LMFDB) 2.139.z_po $6$ (not in LMFDB) 2.139.bi_vu $6$ (not in LMFDB)