Invariants
Base field: | $\F_{163}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 44 x + 808 x^{2} - 7172 x^{3} + 26569 x^{4}$ |
Frobenius angles: | $\pm0.130626345571$, $\pm0.201519655325$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1515776.1 |
Galois group: | $D_{4}$ |
Jacobians: | $24$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $20162$ | $697484228$ | $18755185824626$ | $498344828109050384$ | $13239750128519234222082$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $120$ | $26250$ | $4330704$ | $705959094$ | $115064609200$ | $18755383175130$ | $3057125378460840$ | $498311415228623454$ | $81224760534179536632$ | $13239635966919871038250$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=52x^6+120x^5+13x^4+80x^3+102x^2+31x+31$
- $y^2=50x^6+83x^5+140x^4+3x^3+99x^2+129x+110$
- $y^2=72x^6+6x^5+16x^4+151x^3+69x^2+x+19$
- $y^2=124x^6+107x^5+125x^4+34x^3+43x^2+85x+12$
- $y^2=105x^6+49x^5+135x^4+71x^3+141x^2+7x+42$
- $y^2=53x^6+62x^5+76x^4+9x^3+54x^2+21x+102$
- $y^2=160x^6+91x^5+124x^4+159x^3+136x^2+75x+9$
- $y^2=27x^6+58x^5+157x^4+23x^3+52x^2+56x+108$
- $y^2=12x^6+13x^5+128x^4+4x^3+31x^2+157x+64$
- $y^2=31x^6+2x^5+70x^4+132x^3+118x^2+140x+68$
- $y^2=86x^6+77x^5+18x^4+146x^3+121x^2+54x+72$
- $y^2=118x^6+131x^5+58x^4+155x^3+151x^2+154x+147$
- $y^2=37x^6+98x^5+100x^4+158x^3+141x^2+14x+12$
- $y^2=20x^6+147x^5+86x^4+46x^3+71x^2+34x+29$
- $y^2=67x^6+27x^5+47x^4+111x^3+83x^2+47x+13$
- $y^2=91x^6+55x^5+41x^4+30x^3+117x^2+32x+107$
- $y^2=117x^6+134x^5+55x^4+132x^3+68x^2+118x+79$
- $y^2=48x^6+19x^5+95x^4+147x^3+126x^2+77x+43$
- $y^2=6x^6+32x^5+94x^4+146x^3+72x^2+9x+107$
- $y^2=101x^6+73x^5+20x^4+61x^3+4x^2+129x+104$
- $y^2=38x^6+159x^5+128x^4+31x^3+140x^2+61x+102$
- $y^2=14x^6+77x^5+77x^4+44x^3+94x^2+131x+80$
- $y^2=156x^6+121x^5+154x^4+138x^3+96x^2+39x+63$
- $y^2=97x^6+104x^5+22x^4+20x^3+140x^2+95x+74$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{163}$.
Endomorphism algebra over $\F_{163}$The endomorphism algebra of this simple isogeny class is 4.0.1515776.1. |
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 |
---|---|---|
2.163.bs_bfc | $2$ | (not in LMFDB) |