Properties

 Label 2.113.abm_wo Base field $\F_{113}$ Dimension $2$ $p$-rank $2$ Ordinary Yes Supersingular No Simple No Geometrically simple No Primitive Yes Principally polarizable Yes Contains a Jacobian Yes

Invariants

 Base field: $\F_{113}$ Dimension: $2$ L-polynomial: $( 1 - 20 x + 113 x^{2} )( 1 - 18 x + 113 x^{2} )$ Frobenius angles: $\pm0.110150159186$, $\pm0.178616545187$ Angle rank: $2$ (numerical) Jacobians: 16

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 16 curves, and hence is principally polarizable:

• $y^2=78x^6+10x^5+75x^4+45x^3+86x^2+70x+43$
• $y^2=18x^6+106x^5+74x^4+26x^3+74x^2+106x+18$
• $y^2=108x^6+60x^5+110x^4+24x^3+43x^2+85x+67$
• $y^2=26x^6+59x^5+25x^4+24x^3+25x^2+59x+26$
• $y^2=x^6+8x^5+42x^4+94x^3+42x^2+8x+1$
• $y^2=93x^6+19x^5+13x^4+100x^3+13x^2+19x+93$
• $y^2=9x^6+75x^5+73x^4+103x^3+73x^2+75x+9$
• $y^2=108x^6+29x^5+102x^4+75x^3+51x^2+92x+70$
• $y^2=84x^6+17x^5+53x^4+33x^3+53x^2+17x+84$
• $y^2=31x^6+20x^5+55x^4+65x^3+55x^2+20x+31$
• $y^2=9x^6+19x^5+17x^4+31x^3+40x^2+70x+7$
• $y^2=26x^6+45x^5+93x^4+91x^3+108x^2+24x+11$
• $y^2=52x^6+34x^5+32x^4+6x^3+105x^2+101x+91$
• $y^2=51x^6+59x^5+93x^4+32x^3+34x^2+27x+49$
• $y^2=42x^6+37x^5+28x^4+36x^3+28x^2+37x+42$
• $y^2=108x^6+67x^5+30x^4+94x^3+30x^2+67x+108$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 9024 159616512 2080583555904 26586267657928704 339462255327893461824 4334531865816261955862016 55347535993680814193614132032 706732562671514325559667471155200 9024267972125914158703108097235974976 115230877649321093035728983887049946865152

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 76 12498 1441948 163058558 18424651196 2081955962898 235260592792364 26584442304912766 3004041940300359724 339456738998371396818

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
 The isogeny class factors as 1.113.au $\times$ 1.113.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 $\F_{113}$.

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 2.113.ac_afe $2$ (not in LMFDB) 2.113.c_afe $2$ (not in LMFDB) 2.113.bm_wo $2$ (not in LMFDB)