Invariants
Base field: | $\F_{113}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 36 x + 542 x^{2} - 4068 x^{3} + 12769 x^{4}$ |
Frobenius angles: | $\pm0.0642676148061$, $\pm0.247058548138$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.64512.5 |
Galois group: | $D_{4}$ |
Jacobians: | $28$ |
Isomorphism classes: | 44 |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $9208$ | $160366528$ | $2081483878648$ | $26585724661300224$ | $339457773048401796088$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $78$ | $12558$ | $1442574$ | $163055230$ | $18424407918$ | $2081950897614$ | $235260522989934$ | $26584441618342270$ | $3004041936183250446$ | $339456739004791201038$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 28 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=42x^6+71x^5+55x^4+105x^3+89x^2+34x+18$
- $y^2=63x^6+5x^5+22x^4+87x^3+103x^2+11x+8$
- $y^2=6x^6+49x^5+86x^4+72x^3+7x^2+40x+64$
- $y^2=108x^6+40x^5+17x^4+99x^3+75x^2+14x+82$
- $y^2=34x^6+10x^5+10x^4+91x^3+109x^2+27x+20$
- $y^2=12x^6+x^5+81x^4+95x^3+100x^2+22x+38$
- $y^2=89x^6+8x^5+28x^4+50x^3+68x^2+93x+37$
- $y^2=17x^6+105x^5+76x^4+13x^3+103x^2+108x+5$
- $y^2=53x^6+58x^5+35x^4+83x^3+97x^2+67$
- $y^2=79x^6+102x^5+52x^4+61x^3+94x^2+38x+80$
- $y^2=10x^6+82x^5+82x^4+24x^3+46x^2+62x+67$
- $y^2=71x^6+108x^5+12x^4+97x^3+60x^2+79x+55$
- $y^2=38x^6+93x^5+17x^4+22x^3+73x^2+11x+10$
- $y^2=54x^6+84x^5+4x^4+14x^3+14x^2+49x+92$
- $y^2=58x^6+107x^5+44x^4+86x^3+36x^2+40x+56$
- $y^2=52x^6+92x^5+32x^4+96x^3+58x^2+70x+76$
- $y^2=14x^6+80x^5+22x^4+32x^3+72x^2+36x+6$
- $y^2=14x^5+84x^4+59x^3+100x^2+23x+48$
- $y^2=82x^6+16x^5+44x^4+5x^3+62x^2+71x+78$
- $y^2=33x^6+100x^5+110x^4+91x^3+45x^2+68x+28$
- $y^2=11x^6+78x^5+48x^4+36x^3+64x^2+55x+17$
- $y^2=74x^6+90x^5+67x^4+17x^3+102x^2+106x+8$
- $y^2=35x^6+86x^5+14x^4+32x^3+35x^2+30x+62$
- $y^2=41x^6+95x^5+65x^4+13x^3+30x^2+59x+110$
- $y^2=26x^6+88x^5+81x^4+81x^3+85x^2+54x+105$
- $y^2=12x^6+52x^5+36x^4+27x^3+23x^2+64x+26$
- $y^2=65x^6+18x^5+96x^4+40x^3+37x^2+83x+94$
- $y^2=73x^6+21x^5+78x^4+28x^3+13x^2+48x+20$
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 4.0.64512.5. |
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.bk_uw | $2$ | (not in LMFDB) |