Invariants
Base field: | $\F_{113}$ |
Dimension: | $2$ |
L-polynomial: | $( 1 - 21 x + 113 x^{2} )( 1 - 13 x + 113 x^{2} )$ |
$1 - 34 x + 499 x^{2} - 3842 x^{3} + 12769 x^{4}$ | |
Frobenius angles: | $\pm0.0498602789898$, $\pm0.290579079721$ |
Angle rank: | $2$ (numerical) |
Jacobians: | $36$ |
Isomorphism classes: | 102 |
This isogeny class is not simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.
Newton polygon
This isogeny class is ordinary.
$p$-rank: | $2$ |
Slopes: | $[0, 0, 1, 1]$ |
Point counts
Point counts of the abelian variety
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $9393$ | $161042985$ | $2082048021648$ | $26584702995940425$ | $339453931997677361073$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $80$ | $12612$ | $1442966$ | $163048964$ | $18424199440$ | $2081948051934$ | $235260503533072$ | $26584441656502276$ | $3004041938655930998$ | $339456739027307112132$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 36 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=67x^6+69x^5+51x^4+13x^3+44x^2+44x+70$
- $y^2=38x^6+12x^5+22x^4+55x^3+52x^2+110x+70$
- $y^2=3x^6+30x^5+84x^4+87x^3+3x^2+78x+55$
- $y^2=4x^6+19x^5+72x^4+12x^3+47x^2+33x+90$
- $y^2=82x^6+60x^5+19x^4+8x^3+28x^2+74x+2$
- $y^2=107x^6+79x^5+80x^4+57x^3+47x^2+90x+65$
- $y^2=54x^6+78x^5+67x^4+38x^3+3x^2+83x+72$
- $y^2=20x^6+54x^5+77x^4+70x^3+89x^2+103x+87$
- $y^2=63x^6+18x^5+104x^4+54x^3+72x^2+64x+64$
- $y^2=73x^6+16x^5+83x^4+12x^3+59x^2+109x+96$
- $y^2=53x^6+19x^5+16x^4+92x^3+52x^2+69x+101$
- $y^2=80x^6+8x^5+96x^4+18x^3+6x^2+77x+21$
- $y^2=53x^6+79x^5+57x^4+93x^3+13x^2+25x+67$
- $y^2=30x^6+54x^5+91x^4+17x^3+27x^2+11x+34$
- $y^2=47x^6+45x^5+95x^4+86x^3+44x^2+63x+104$
- $y^2=86x^6+18x^5+50x^4+78x^3+74x^2+102x+9$
- $y^2=84x^6+97x^5+100x^4+59x^3+22x^2+103x+43$
- $y^2=71x^6+10x^5+98x^4+4x^3+72x^2+27x+20$
- $y^2=19x^6+87x^5+58x^4+75x^3+70x^2+41x+65$
- $y^2=109x^6+5x^5+106x^4+92x^3+51x^2+74x+102$
- and 16 more
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{113}$.
Endomorphism algebra over $\F_{113}$The isogeny class factors as 1.113.av $\times$ 1.113.an and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is: |
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.ai_abv | $2$ | (not in LMFDB) |
2.113.i_abv | $2$ | (not in LMFDB) |
2.113.bi_tf | $2$ | (not in LMFDB) |