Invariants
| Base field: | $\F_{157}$ |
| Dimension: | $2$ |
| L-polynomial: | $( 1 - 25 x + 157 x^{2} )( 1 - 17 x + 157 x^{2} )$ |
| $1 - 42 x + 739 x^{2} - 6594 x^{3} + 24649 x^{4}$ | |
| Frobenius angles: | $\pm0.0220179720414$, $\pm0.262684997750$ |
| Angle rank: | $2$ (numerical) |
| Jacobians: | $24$ |
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
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ |
|---|---|---|---|---|---|
| $A(\F_{q^r})$ | $18753$ | $600564825$ | $14973142019472$ | $369145952946815625$ | $9099037060900462777353$ |
| $r$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ | $9$ | $10$ |
|---|---|---|---|---|---|---|---|---|---|---|
| $C(\F_{q^r})$ | $116$ | $24364$ | $3869138$ | $607574452$ | $95388753116$ | $14976062915686$ | $2351243106900188$ | $369145192385677348$ | $57955795529350311866$ | $9099059900966503830364$ |
Jacobians and polarizations
This isogeny class contains the Jacobians of 24 curves (of which all are hyperelliptic), and hence is principally polarizable:
- $y^2=109x^6+146x^5+3x^4+112x^3+140x^2+86x+94$
- $y^2=70x^6+34x^5+68x^4+100x^3+95x^2+100x+64$
- $y^2=40x^6+89x^5+41x^4+7x^3+116x^2+115x+56$
- $y^2=155x^6+42x^5+4x^4+108x^3+44x^2+58x+7$
- $y^2=29x^6+106x^5+86x^4+73x^3+75x^2+58x+23$
- $y^2=83x^6+71x^5+152x^4+69x^3+127x^2+113x+20$
- $y^2=125x^6+100x^5+x^4+101x^3+71x^2+40x+68$
- $y^2=117x^6+107x^5+8x^4+69x^3+12x^2+85x+32$
- $y^2=15x^6+101x^5+97x^4+47x^3+54x^2+122x+96$
- $y^2=152x^6+149x^5+16x^4+95x^3+18x^2+11x+124$
- $y^2=63x^6+113x^5+70x^4+57x^3+123x^2+132x+54$
- $y^2=84x^6+106x^5+10x^4+156x^3+42x^2+9x+147$
- $y^2=49x^6+12x^5+107x^4+144x^3+80x^2+37x+156$
- $y^2=152x^6+7x^5+71x^4+19x^3+114x^2+80x+155$
- $y^2=3x^6+138x^5+58x^4+149x^3+125x^2+16x+83$
- $y^2=54x^6+12x^5+98x^4+39x^3+65x^2+36x+55$
- $y^2=102x^6+122x^5+64x^4+143x^3+123x^2+81x+99$
- $y^2=83x^6+78x^5+31x^4+64x^3+117x^2+12x+1$
- $y^2=60x^6+35x^5+58x^4+107x^3+117x^2+93x+95$
- $y^2=82x^6+64x^5+64x^4+133x^3+144x^2+10x+46$
- $y^2=60x^6+93x^5+19x^4+53x^3+39x^2+40x+142$
- $y^2=17x^6+33x^5+31x^4+29x^3+62x^2+41x+62$
- $y^2=25x^6+5x^5+75x^4+23x^3+2x^2+126x+65$
- $y^2=60x^6+92x^5+125x^4+40x^3+70x^2+60x+97$
Decomposition and endomorphism algebra
All geometric endomorphisms are defined over $\F_{157}$.
Endomorphism algebra over $\F_{157}$| The isogeny class factors as 1.157.az $\times$ 1.157.ar 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.