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 |
1.11.ag |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 6 x + 11 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$6$ |
$[6, 108, 1314, 14688, 161526, 1773900, 19495986, 214386048, 2358013734, 25937522028]$ |
$6$ |
$[6, 108, 1314, 14688, 161526, 1773900, 19495986, 214386048, 2358013734, 25937522028]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$C_2$ |
simple |
1.11.af |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 5 x + 11 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$7$ |
$[7, 119, 1372, 14875, 161777, 1772624, 19484507, 214333875, 2357851972, 25937221079]$ |
$7$ |
$[7, 119, 1372, 14875, 161777, 1772624, 19484507, 214333875, 2357851972, 25937221079]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \) |
$C_2$ |
simple |
1.11.ae |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 4 x + 11 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$8$ |
$[8, 128, 1400, 14848, 161128, 1769600, 19478488, 214345728, 2357990600, 25937740928]$ |
$8$ |
$[8, 128, 1400, 14848, 161128, 1769600, 19478488, 214345728, 2357990600, 25937740928]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
simple |
1.11.ad |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 11 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$9$ |
$[9, 135, 1404, 14715, 160479, 1769040, 19485909, 214382835, 2358033444, 25937418375]$ |
$9$ |
$[9, 135, 1404, 14715, 160479, 1769040, 19485909, 214382835, 2358033444, 25937418375]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-35}) \) |
$C_2$ |
simple |
1.11.ac |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 11 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$10$ |
$[10, 140, 1390, 14560, 160250, 1770860, 19494590, 214381440, 2357911210, 25937103500]$ |
$10$ |
$[10, 140, 1390, 14560, 160250, 1770860, 19494590, 214381440, 2357911210, 25937103500]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$C_2$ |
simple |
1.11.ab |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x + 11 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$11$ |
$[11, 143, 1364, 14443, 160501, 1773200, 19494871, 214348563, 2357852684, 25937443103]$ |
$11$ |
$[11, 143, 1364, 14443, 160501, 1773200, 19494871, 214348563, 2357852684, 25937443103]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
simple |
1.11.a |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
|
✓ |
✓ |
✓ |
✓ |
$1 + 11 x^{2}$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$1$ |
$0$ |
$1$ |
$0$ |
$1$ |
$12$ |
$[12, 144, 1332, 14400, 161052, 1774224, 19487172, 214329600, 2357947692, 25937746704]$ |
$12$ |
$[12, 144, 1332, 14400, 161052, 1774224, 19487172, 214329600, 2357947692, 25937746704]$ |
$4$ |
$0$ |
$1$ |
$1$ |
$2$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
simple |
1.11.b |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + x + 11 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$13$ |
$[13, 143, 1300, 14443, 161603, 1773200, 19479473, 214348563, 2358042700, 25937443103]$ |
$13$ |
$[13, 143, 1300, 14443, 161603, 1773200, 19479473, 214348563, 2358042700, 25937443103]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
simple |
1.11.c |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 2 x + 11 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$14$ |
$[14, 140, 1274, 14560, 161854, 1770860, 19479754, 214381440, 2357984174, 25937103500]$ |
$14$ |
$[14, 140, 1274, 14560, 161854, 1770860, 19479754, 214381440, 2357984174, 25937103500]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$C_2$ |
simple |
1.11.d |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 3 x + 11 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$15$ |
$[15, 135, 1260, 14715, 161625, 1769040, 19488435, 214382835, 2357861940, 25937418375]$ |
$15$ |
$[15, 135, 1260, 14715, 161625, 1769040, 19488435, 214382835, 2357861940, 25937418375]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-35}) \) |
$C_2$ |
simple |
1.11.e |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 4 x + 11 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$16$ |
$[16, 128, 1264, 14848, 160976, 1769600, 19495856, 214345728, 2357904784, 25937740928]$ |
$16$ |
$[16, 128, 1264, 14848, 160976, 1769600, 19495856, 214345728, 2357904784, 25937740928]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
simple |
1.11.f |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 5 x + 11 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$17$ |
$[17, 119, 1292, 14875, 160327, 1772624, 19489837, 214333875, 2358043412, 25937221079]$ |
$17$ |
$[17, 119, 1292, 14875, 160327, 1772624, 19489837, 214333875, 2358043412, 25937221079]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \) |
$C_2$ |
simple |
1.11.g |
$1$ |
$\F_{11}$ |
$11$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 6 x + 11 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$18$ |
$[18, 108, 1350, 14688, 160578, 1773900, 19478358, 214386048, 2357881650, 25937522028]$ |
$18$ |
$[18, 108, 1350, 14688, 160578, 1773900, 19478358, 214386048, 2357881650, 25937522028]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$C_2$ |
simple |