| Label |
Dimension |
Base field |
Base char. |
Simple |
Geom. simple |
Primitive |
Ordinary |
Almost ordinary |
Supersingular |
Princ. polarizable |
Jacobian |
L-polynomial |
Newton slopes |
Newton elevation |
$p$-rank |
$p$-corank |
Angle rank |
Angle corank |
$\mathbb{F}_q$ points on curve |
$\mathbb{F}_{q^k}$ points on curve |
$\mathbb{F}_q$ points on variety |
$\mathbb{F}_{q^k}$ points on variety |
Jacobians |
Hyperelliptic Jacobians |
Num. twists |
Max. twist degree |
End. degree |
Number fields |
Galois groups |
Isogeny factors |
| 5.3.ad_h_ae_ap_bp |
$5$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - x + 3 x^{2} )^{3}( 1 - 5 x^{2} + 9 x^{4} )$ |
$[0,0,0,0,0,1,1,1,1,1]$ |
$0$ |
$5$ |
$0$ |
$1$ |
$4$ |
$1$ |
$[1, 15, 52, 47, 151, 720, 2437, 7127, 19276, 58575]$ |
$135$ |
$[135, 84375, 34525440, 2373046875, 575225611425, 204390604800000, 56050225211162835, 13251234825263671875, 2893784469053900855040, 712091333065895771484375]$ |
$None$ |
$0$ |
$42$ |
$44$ |
$4$ |
\(\Q(\sqrt{-11}) \), \(\Q(i, \sqrt{11})\) |
$C_2$, $C_2^2$ |
1.3.ab 3 $\times$ 2.3.a_af |
| 5.3.ab_ah_k_n_abr |
$5$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 3 x^{2} )( 1 - 5 x^{2} + 9 x^{4} )^{2}$ |
$[0,0,0,0,0,1,1,1,1,1]$ |
$0$ |
$5$ |
$0$ |
$1$ |
$4$ |
$3$ |
$[3, -5, 36, 47, 213, 760, 2271, 7127, 19548, 60475]$ |
$75$ |
$[75, 9375, 19713600, 2373046875, 754707058125, 215903347200000, 52007868242145975, 13251234825263671875, 2933733845082470731200, 735376781622137724609375]$ |
$None$ |
$0$ |
$42$ |
$44$ |
$4$ |
\(\Q(\sqrt{-11}) \), \(\Q(i, \sqrt{11})\) |
$C_2$, $C_2^2$ |
1.3.ab $\times$ 2.3.a_af 2 |
| 5.3.ab_d_a_ah_h |
$5$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 + x + 3 x^{2} )( 1 - x + 3 x^{2} )^{2}( 1 - 5 x^{2} + 9 x^{4} )$ |
$[0,0,0,0,0,1,1,1,1,1]$ |
$0$ |
$5$ |
$0$ |
$1$ |
$4$ |
$3$ |
$[3, 15, 36, 47, 213, 720, 2271, 7127, 19548, 58575]$ |
$225$ |
$[225, 84375, 19180800, 2373046875, 742662174375, 204390604800000, 51953203024877925, 13251234825263671875, 2934049937418063993600, 712091333065895771484375]$ |
$None$ |
$0$ |
$42$ |
$44$ |
$4$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-11}) \), \(\Q(i, \sqrt{11})\) |
$C_2$, $C_2$, $C_2^2$ |
1.3.ab 2 $\times$ 1.3.b $\times$ 2.3.a_af |
| 5.3.b_ah_ak_n_br |
$5$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 + x + 3 x^{2} )( 1 - 5 x^{2} + 9 x^{4} )^{2}$ |
$[0,0,0,0,0,1,1,1,1,1]$ |
$0$ |
$5$ |
$0$ |
$1$ |
$4$ |
$5$ |
$[5, -5, 20, 47, 275, 760, 2105, 7127, 19820, 60475]$ |
$125$ |
$[125, 9375, 10952000, 2373046875, 974387046875, 215903347200000, 48206324372398625, 13251234825263671875, 2974555187719182008000, 735376781622137724609375]$ |
$None$ |
$0$ |
$42$ |
$44$ |
$4$ |
\(\Q(\sqrt{-11}) \), \(\Q(i, \sqrt{11})\) |
$C_2$, $C_2^2$ |
1.3.b $\times$ 2.3.a_af 2 |
| 5.3.b_d_a_ah_ah |
$5$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
? |
$( 1 - x + 3 x^{2} )( 1 + x + 3 x^{2} )^{2}( 1 - 5 x^{2} + 9 x^{4} )$ |
$[0,0,0,0,0,1,1,1,1,1]$ |
$0$ |
$5$ |
$0$ |
$1$ |
$4$ |
$5$ |
$[5, 15, 20, 47, 275, 720, 2105, 7127, 19820, 58575]$ |
$375$ |
$[375, 84375, 10656000, 2373046875, 958836140625, 204390604800000, 48155654939395875, 13251234825263671875, 2974875678311133024000, 712091333065895771484375]$ |
$None$ |
$0$ |
$42$ |
$44$ |
$4$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-11}) \), \(\Q(i, \sqrt{11})\) |
$C_2$, $C_2$, $C_2^2$ |
1.3.ab $\times$ 1.3.b 2 $\times$ 2.3.a_af |
| 5.3.d_h_e_ap_abp |
$5$ |
$\F_{3}$ |
$3$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 + x + 3 x^{2} )^{3}( 1 - 5 x^{2} + 9 x^{4} )$ |
$[0,0,0,0,0,1,1,1,1,1]$ |
$0$ |
$5$ |
$0$ |
$1$ |
$4$ |
$7$ |
$[7, 15, 4, 47, 337, 720, 1939, 7127, 20092, 58575]$ |
$625$ |
$[625, 84375, 5920000, 2373046875, 1237933984375, 204390604800000, 44635690729823125, 13251234825263671875, 3016269487626696160000, 712091333065895771484375]$ |
$None$ |
$0$ |
$42$ |
$44$ |
$4$ |
\(\Q(\sqrt{-11}) \), \(\Q(i, \sqrt{11})\) |
$C_2$, $C_2^2$ |
1.3.b 3 $\times$ 2.3.a_af |
