Properties

 Label 2.107.abk_ur Base Field $\F_{107}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{107}$ Dimension: $2$ L-polynomial: $( 1 - 19 x + 107 x^{2} )( 1 - 17 x + 107 x^{2} )$ Frobenius angles: $\pm0.129482033963$, $\pm0.193011390838$ Angle rank: $2$ (numerical) Jacobians: 9

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 9 curves, and hence is principally polarizable:

• $y^2=34x^6+74x^5+100x^4+55x^3+10x^2+20x+79$
• $y^2=99x^6+24x^5+77x^4+13x^3+8x^2+103x+90$
• $y^2=59x^6+38x^5+87x^4+52x^3+105x^2+71x+71$
• $y^2=72x^6+28x^5+36x^4+74x^3+19x^2+22x+91$
• $y^2=72x^6+35x^5+4x^4+39x^3+33x^2+75x+50$
• $y^2=37x^6+97x^5+102x^4+61x^3+49x^2+24x+87$
• $y^2=32x^6+31x^5+14x^4+30x^3+52x^2+63x+31$
• $y^2=79x^6+40x^5+37x^4+106x^3+86x^2+25x+75$
• $y^2=59x^6+89x^5+58x^4+45x^3+38x^2+48x+106$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 8099 128571625 1500467778992 17184295182315625 196719921905547219179 2252197631862719466016000 25785347232192236264243084963 295216378710438436416146153615625 3379932276680887518080914521341102768 38696844622791836935477278423506658945625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 72 11228 1224828 131098164 14025858552 1500734378486 160578183332520 17181862022619556 1838459212935995556 196715135718433936268

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{107}$
 The isogeny class factors as 1.107.at $\times$ 1.107.ar 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 $\F_{107}$.

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 2.107.ac_aef $2$ (not in LMFDB) 2.107.c_aef $2$ (not in LMFDB) 2.107.bk_ur $2$ (not in LMFDB)