Invariants
| Base field: | $\F_{113}$ |
| Dimension: | $2$ |
| L-polynomial: | $1 - 35 x + 523 x^{2} - 3955 x^{3} + 12769 x^{4}$ |
| Frobenius angles: | $\pm0.0830136176920$, $\pm0.261946670442$ |
| Angle rank: | $2$ (numerical) |
| Number field: | 4.0.9995069.2 |
| Galois group: | $D_{4}$ |
| Jacobians: | $28$ |
| Isomorphism classes: | 28 |
This isogeny class is simple and geometrically 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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $9303$ | $160783749$ | $2082203944191$ | $26586462576448341$ | $339458235075501078768$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $79$ | $12591$ | $1443073$ | $163059755$ | $18424432994$ | $2081951090847$ | $235260529195253$ | $26584441778331379$ | $3004041938912822299$ | $339456739037455057086$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=35x^6+31x^5+48x^4+11x^3+98x^2+38x+7$
- $y^2=99x^6+8x^5+35x^4+98x^3+3x^2+97x+79$
- $y^2=45x^6+91x^5+43x^4+101x^3+79x^2+23x+44$
- $y^2=83x^6+104x^5+33x^4+73x^3+18x^2+86x+87$
- $y^2=78x^6+100x^5+34x^4+50x^3+85x^2+27x+112$
- $y^2=73x^6+61x^5+10x^4+61x^3+8x^2+37x+9$
- $y^2=29x^6+75x^5+92x^4+40x^3+99x^2+73x+34$
- $y^2=10x^6+70x^5+40x^4+53x^3+11x^2+63x+47$
- $y^2=47x^6+8x^5+90x^4+30x^3+106x^2+82x+24$
- $y^2=108x^6+2x^5+22x^4+67x^3+31x^2+96x+15$
- $y^2=68x^6+66x^5+28x^4+65x^3+51x^2+96x+27$
- $y^2=92x^6+33x^5+94x^4+112x^3+100x^2+46x+88$
- $y^2=52x^6+61x^5+34x^4+5x^3+107x^2+79x+94$
- $y^2=58x^6+76x^5+63x^4+71x^3+38x^2+101x+62$
- $y^2=17x^6+96x^5+36x^4+16x^3+93x^2+7x+54$
- $y^2=3x^6+32x^5+8x^4+23x^3+101x^2+104x+101$
- $y^2=103x^6+19x^5+89x^4+48x^3+27x^2+35x+86$
- $y^2=12x^6+33x^5+71x^4+72x^3+13x^2+74x+3$
- $y^2=20x^6+x^5+67x^3+103x^2+49x+20$
- $y^2=81x^6+3x^5+19x^3+5x^2+90x+73$
- $y^2=43x^6+73x^5+7x^4+69x^3+4x^2+8x+59$
- $y^2=109x^6+42x^5+50x^4+99x^3+65x^2+20x+32$
- $y^2=100x^6+64x^5+67x^4+23x^3+82x^2+77x+56$
- $y^2=71x^6+64x^5+40x^4+36x^3+66x^2+23x+64$
- $y^2=36x^6+35x^5+14x^4+40x^3+67x^2+4x+20$
- $y^2=38x^6+68x^5+21x^4+3x^3+66x^2+19x+83$
- $y^2=107x^6+65x^5+21x^4+90x^3+89x^2+79x+58$
- $y^2=105x^6+59x^5+80x^4+63x^3+13x^2+106x+34$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{113}$.
Endomorphism algebra over $\F_{113}$| The endomorphism algebra of this simple isogeny class is 4.0.9995069.2. |
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.bj_ud | $2$ | (not in LMFDB) |