Invariants
Base field: | $\F_{181}$ |
Dimension: | $2$ |
L-polynomial: | $1 - 46 x + 883 x^{2} - 8326 x^{3} + 32761 x^{4}$ |
Frobenius angles: | $\pm0.0904413448067$, $\pm0.230211930735$ |
Angle rank: | $2$ (numerical) |
Number field: | 4.0.1154624.2 |
Galois group: | $D_{4}$ |
Jacobians: | $27$ |
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
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
---|---|---|---|---|---|
$A(\F_{q^r})$ | $25273$ | $1061895641$ | $35159103704512$ | $1151975229868110281$ | $37738723552986352597873$ |
$r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
---|---|---|---|---|---|---|---|---|---|---|
$C(\F_{q^r})$ | $136$ | $32412$ | $5929282$ | $1073319060$ | $194264897136$ | $35161834232982$ | $6364290937240288$ | $1151936657323503204$ | $208500535061994312442$ | $37738596847100572683052$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 27 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=79x^6+88x^5+164x^4+123x^3+89x^2+128x+30$
- $y^2=86x^6+169x^5+174x^4+99x^3+81x^2+21x+2$
- $y^2=43x^6+152x^5+117x^4+50x^3+4x^2+18x+101$
- $y^2=47x^6+140x^5+103x^4+135x^3+99x^2+52x+97$
- $y^2=170x^6+142x^5+58x^4+171x^3+64x^2+64x+115$
- $y^2=110x^6+39x^5+132x^4+169x^3+59x^2+108x+17$
- $y^2=76x^6+114x^5+61x^4+42x^3+136x^2+85x+92$
- $y^2=69x^6+106x^5+38x^4+132x^3+86x^2+48x+24$
- $y^2=107x^6+48x^5+175x^4+19x^3+80x^2+86x+106$
- $y^2=28x^6+71x^5+90x^4+141x^3+15x^2+173x+105$
- $y^2=150x^6+58x^5+60x^4+95x^3+31x^2+34x+55$
- $y^2=80x^6+121x^5+142x^4+38x^3+15x^2+93x+7$
- $y^2=152x^6+106x^5+59x^4+52x^3+3x^2+58x+159$
- $y^2=83x^6+76x^5+8x^4+62x^3+131x^2+54x+8$
- $y^2=144x^6+36x^5+4x^4+93x^3+51x^2+103x+66$
- $y^2=123x^6+15x^5+65x^4+145x^3+34x^2+100x+173$
- $y^2=99x^6+140x^5+167x^4+138x^3+22x^2+138x+94$
- $y^2=125x^6+60x^5+38x^4+161x^3+164x^2+63x+170$
- $y^2=40x^6+162x^5+83x^4+14x^3+134x^2+92x+83$
- $y^2=118x^6+127x^5+3x^4+97x^3+64x^2+111x+168$
- $y^2=60x^6+82x^5+15x^4+11x^3+79x^2+123x+18$
- $y^2=140x^6+24x^5+169x^4+113x^3+101x^2+15x+91$
- $y^2=162x^6+155x^5+158x^4+132x^3+62x^2+94x+128$
- $y^2=78x^6+138x^5+112x^4+57x^3+168x^2+163x+114$
- $y^2=134x^6+162x^5+10x^4+27x^3+126x^2+175x+110$
- $y^2=46x^6+146x^5+x^4+62x^3+116x^2+168x+18$
- $y^2=14x^6+48x^5+83x^4+88x^3+100x^2+164x+172$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{181}$.
Endomorphism algebra over $\F_{181}$The endomorphism algebra of this simple isogeny class is 4.0.1154624.2. |
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 |
---|---|---|
2.181.bu_bhz | $2$ | (not in LMFDB) |