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 |
1.41.am |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 12 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$30$ |
$[30, 1620, 68670, 2825280, 115860750, 4750178580, 194754979470, 7984930648320, 327381970495230, 13422659521180500]$ |
$30$ |
$[30, 1620, 68670, 2825280, 115860750, 4750178580, 194754979470, 7984930648320, 327381970495230, 13422659521180500]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-5}) \) |
$C_2$ |
simple |
1.41.al |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$31$ |
$[31, 1643, 68944, 2827603, 115875551, 4750241600, 194754991511, 7984927491363, 327381929855824, 13422659167481003]$ |
$31$ |
$[31, 1643, 68944, 2827603, 115875551, 4750241600, 194754991511, 7984927491363, 327381929855824, 13422659167481003]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
simple |
1.41.ak |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$32$ |
$[32, 1664, 69152, 2828800, 115877152, 4750189184, 194754264352, 7984921651200, 327381899005472, 13422659102962304]$ |
$32$ |
$[32, 1664, 69152, 2828800, 115877152, 4750189184, 194754264352, 7984921651200, 327381899005472, 13422659102962304]$ |
$4$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
1.41.aj |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$33$ |
$[33, 1683, 69300, 2829123, 115870953, 4750099200, 194753623713, 7984919584323, 327381910247700, 13422659324272803]$ |
$33$ |
$[33, 1683, 69300, 2829123, 115870953, 4750099200, 194753623713, 7984919584323, 327381910247700, 13422659324272803]$ |
$3$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$C_2$ |
simple |
1.41.ai |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$34$ |
$[34, 1700, 69394, 2828800, 115861154, 4750019300, 194753391314, 7984921651200, 327381941955874, 13422659517342500]$ |
$34$ |
$[34, 1700, 69394, 2828800, 115861154, 4750019300, 194753391314, 7984921651200, 327381941955874, 13422659517342500]$ |
$3$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
1.41.ah |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$35$ |
$[35, 1715, 69440, 2828035, 115850875, 4749973760, 194753578915, 7984925714115, 327381966282560, 13422659513487875]$ |
$35$ |
$[35, 1715, 69440, 2828035, 115850875, 4749973760, 194753578915, 7984925714115, 327381966282560, 13422659513487875]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-115}) \) |
$C_2$ |
simple |
1.41.ag |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 6 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$36$ |
$[36, 1728, 69444, 2827008, 115842276, 4749969600, 194754036996, 7984929328128, 327381968700324, 13422659347931328]$ |
$36$ |
$[36, 1728, 69444, 2827008, 115842276, 4749969600, 194754036996, 7984929328128, 327381968700324, 13422659347931328]$ |
$7$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$C_2$ |
simple |
1.41.af |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 5 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$37$ |
$[37, 1739, 69412, 2825875, 115836677, 4750001984, 194754563117, 7984930867875, 327381950729092, 13422659160639179]$ |
$37$ |
$[37, 1739, 69412, 2825875, 115836677, 4750001984, 194754563117, 7984930867875, 327381950729092, 13422659160639179]$ |
$3$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-139}) \) |
$C_2$ |
simple |
1.41.ae |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 4 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$38$ |
$[38, 1748, 69350, 2824768, 115834678, 4750058900, 194754974998, 7984929892608, 327381924302150, 13422659078582228]$ |
$38$ |
$[38, 1748, 69350, 2824768, 115834678, 4750058900, 194754974998, 7984929892608, 327381924302150, 13422659078582228]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-37}) \) |
$C_2$ |
simple |
1.41.ad |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$39$ |
$[39, 1755, 69264, 2823795, 115836279, 4750125120, 194755153359, 7984927011555, 327381903682704, 13422659144938875]$ |
$39$ |
$[39, 1755, 69264, 2823795, 115836279, 4750125120, 194755153359, 7984927011555, 327381903682704, 13422659144938875]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-155}) \) |
$C_2$ |
simple |
1.41.ac |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$40$ |
$[40, 1760, 69160, 2823040, 115841000, 4750185440, 194755059560, 7984923471360, 327381898665640, 13422659310764000]$ |
$40$ |
$[40, 1760, 69160, 2823040, 115841000, 4750185440, 194755059560, 7984923471360, 327381898665640, 13422659310764000]$ |
$6$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$C_2$ |
simple |
1.41.ab |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$41$ |
$[41, 1763, 69044, 2822563, 115848001, 4750227200, 194754733081, 7984920647043, 327381910984724, 13422659474608403]$ |
$41$ |
$[41, 1763, 69044, 2822563, 115848001, 4750227200, 194754733081, 7984920647043, 327381910984724, 13422659474608403]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-163}) \) |
$C_2$ |
simple |
1.41.a |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
|
✓ |
✓ |
✓ |
✓ |
$1 + 41 x^{2}$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$1$ |
$0$ |
$1$ |
$0$ |
$1$ |
$42$ |
$[42, 1764, 68922, 2822400, 115856202, 4750242084, 194754273882, 7984919577600, 327381934393962, 13422659541864804]$ |
$42$ |
$[42, 1764, 68922, 2822400, 115856202, 4750242084, 194754273882, 7984919577600, 327381934393962, 13422659541864804]$ |
$8$ |
$0$ |
$1$ |
$1$ |
$2$ |
\(\Q(\sqrt{-41}) \) |
$C_2$ |
simple |
1.41.b |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$43$ |
$[43, 1763, 68800, 2822563, 115864403, 4750227200, 194753814683, 7984920647043, 327381957803200, 13422659474608403]$ |
$43$ |
$[43, 1763, 68800, 2822563, 115864403, 4750227200, 194753814683, 7984920647043, 327381957803200, 13422659474608403]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-163}) \) |
$C_2$ |
simple |
1.41.c |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 2 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$44$ |
$[44, 1760, 68684, 2823040, 115871404, 4750185440, 194753488204, 7984923471360, 327381970122284, 13422659310764000]$ |
$44$ |
$[44, 1760, 68684, 2823040, 115871404, 4750185440, 194753488204, 7984923471360, 327381970122284, 13422659310764000]$ |
$6$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$C_2$ |
simple |
1.41.d |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 3 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$45$ |
$[45, 1755, 68580, 2823795, 115876125, 4750125120, 194753394405, 7984927011555, 327381965105220, 13422659144938875]$ |
$45$ |
$[45, 1755, 68580, 2823795, 115876125, 4750125120, 194753394405, 7984927011555, 327381965105220, 13422659144938875]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-155}) \) |
$C_2$ |
simple |
1.41.e |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 4 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$46$ |
$[46, 1748, 68494, 2824768, 115877726, 4750058900, 194753572766, 7984929892608, 327381944485774, 13422659078582228]$ |
$46$ |
$[46, 1748, 68494, 2824768, 115877726, 4750058900, 194753572766, 7984929892608, 327381944485774, 13422659078582228]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-37}) \) |
$C_2$ |
simple |
1.41.f |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 5 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$47$ |
$[47, 1739, 68432, 2825875, 115875727, 4750001984, 194753984647, 7984930867875, 327381918058832, 13422659160639179]$ |
$47$ |
$[47, 1739, 68432, 2825875, 115875727, 4750001984, 194753984647, 7984930867875, 327381918058832, 13422659160639179]$ |
$3$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-139}) \) |
$C_2$ |
simple |
1.41.g |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 6 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$48$ |
$[48, 1728, 68400, 2827008, 115870128, 4749969600, 194754510768, 7984929328128, 327381900087600, 13422659347931328]$ |
$48$ |
$[48, 1728, 68400, 2827008, 115870128, 4749969600, 194754510768, 7984929328128, 327381900087600, 13422659347931328]$ |
$7$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$C_2$ |
simple |
1.41.h |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 7 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$49$ |
$[49, 1715, 68404, 2828035, 115861529, 4749973760, 194754968849, 7984925714115, 327381902505364, 13422659513487875]$ |
$49$ |
$[49, 1715, 68404, 2828035, 115861529, 4749973760, 194754968849, 7984925714115, 327381902505364, 13422659513487875]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-115}) \) |
$C_2$ |
simple |
1.41.i |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 8 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$50$ |
$[50, 1700, 68450, 2828800, 115851250, 4750019300, 194755156450, 7984921651200, 327381926832050, 13422659517342500]$ |
$50$ |
$[50, 1700, 68450, 2828800, 115851250, 4750019300, 194755156450, 7984921651200, 327381926832050, 13422659517342500]$ |
$3$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
1.41.j |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 9 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$51$ |
$[51, 1683, 68544, 2829123, 115841451, 4750099200, 194754924051, 7984919584323, 327381958540224, 13422659324272803]$ |
$51$ |
$[51, 1683, 68544, 2829123, 115841451, 4750099200, 194754924051, 7984919584323, 327381958540224, 13422659324272803]$ |
$3$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$C_2$ |
simple |
1.41.k |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 10 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$52$ |
$[52, 1664, 68692, 2828800, 115835252, 4750189184, 194754283412, 7984921651200, 327381969782452, 13422659102962304]$ |
$52$ |
$[52, 1664, 68692, 2828800, 115835252, 4750189184, 194754283412, 7984921651200, 327381969782452, 13422659102962304]$ |
$4$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
1.41.l |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 11 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$53$ |
$[53, 1643, 68900, 2827603, 115836853, 4750241600, 194753556253, 7984927491363, 327381938932100, 13422659167481003]$ |
$53$ |
$[53, 1643, 68900, 2827603, 115836853, 4750241600, 194753556253, 7984927491363, 327381938932100, 13422659167481003]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
simple |
1.41.m |
$1$ |
$\F_{41}$ |
$41$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 12 x + 41 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$54$ |
$[54, 1620, 69174, 2825280, 115851654, 4750178580, 194753568294, 7984930648320, 327381898292694, 13422659521180500]$ |
$54$ |
$[54, 1620, 69174, 2825280, 115851654, 4750178580, 194753568294, 7984930648320, 327381898292694, 13422659521180500]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-5}) \) |
$C_2$ |
simple |