| 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 |
| 1.23.aj |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$15$ |
$[15, 495, 12060, 279675, 6437325, 148048560, 3404916915, 78311517075, 1801155343860, 41426523123975]$ |
$15$ |
$[15, 495, 12060, 279675, 6437325, 148048560, 3404916915, 78311517075, 1801155343860, 41426523123975]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
simple |
| 1.23.ai |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$16$ |
$[16, 512, 12208, 280576, 6441296, 148058624, 3404893424, 78311006208, 1801151265424, 41426499564032]$ |
$16$ |
$[16, 512, 12208, 280576, 6441296, 148058624, 3404893424, 78311006208, 1801151265424, 41426499564032]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
simple |
| 1.23.ah |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$17$ |
$[17, 527, 12308, 280891, 6440467, 148040624, 3404763757, 78310444563, 1801150295324, 41426507087207]$ |
$17$ |
$[17, 527, 12308, 280891, 6440467, 148040624, 3404763757, 78310444563, 1801150295324, 41426507087207]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
simple |
| 1.23.ag |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 6 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$18$ |
$[18, 540, 12366, 280800, 6437538, 148021020, 3404708766, 78310627200, 1801153196658, 41426522660700]$ |
$18$ |
$[18, 540, 12366, 280800, 6437538, 148021020, 3404708766, 78310627200, 1801153196658, 41426522660700]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-14}) \) |
$C_2$ |
simple |
| 1.23.af |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 5 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$19$ |
$[19, 551, 12388, 280459, 6434369, 148011824, 3404750543, 78311164275, 1801155279244, 41426520185711]$ |
$19$ |
$[19, 551, 12388, 280459, 6434369, 148011824, 3404750543, 78311164275, 1801155279244, 41426520185711]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-67}) \) |
$C_2$ |
simple |
| 1.23.ae |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 4 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$20$ |
$[20, 560, 12380, 280000, 6432100, 148015280, 3404840620, 78311520000, 1801154451380, 41426506074800]$ |
$20$ |
$[20, 560, 12380, 280000, 6432100, 148015280, 3404840620, 78311520000, 1801154451380, 41426506074800]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \) |
$C_2$ |
simple |
| 1.23.ad |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$21$ |
$[21, 567, 12348, 279531, 6431271, 148027824, 3404917929, 78311448243, 1801151923284, 41426498351007]$ |
$21$ |
$[21, 567, 12348, 279531, 6431271, 148027824, 3404917929, 78311448243, 1801151923284, 41426498351007]$ |
$3$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$C_2$ |
simple |
| 1.23.ac |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$22$ |
$[22, 572, 12298, 279136, 6431942, 148043324, 3404941562, 78311046528, 1801150113334, 41426504708732]$ |
$22$ |
$[22, 572, 12298, 279136, 6431942, 148043324, 3404941562, 78311046528, 1801150113334, 41426504708732]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-22}) \) |
$C_2$ |
simple |
| 1.23.ab |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$23$ |
$[23, 575, 12236, 278875, 6433813, 148055600, 3404903371, 78310609875, 1801150493828, 41426517680375]$ |
$23$ |
$[23, 575, 12236, 278875, 6433813, 148055600, 3404903371, 78310609875, 1801150493828, 41426517680375]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$C_2$ |
simple |
| 1.23.a |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
|
✓ |
✓ |
✓ |
✓ |
$1 + 23 x^{2}$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$1$ |
$0$ |
$1$ |
$0$ |
$1$ |
$24$ |
$[24, 576, 12168, 278784, 6436344, 148060224, 3404825448, 78310425600, 1801152661464, 41426524086336]$ |
$24$ |
$[24, 576, 12168, 278784, 6436344, 148060224, 3404825448, 78310425600, 1801152661464, 41426524086336]$ |
$6$ |
$0$ |
$1$ |
$1$ |
$2$ |
\(\Q(\sqrt{-23}) \) |
$C_2$ |
simple |
| 1.23.b |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$25$ |
$[25, 575, 12100, 278875, 6438875, 148055600, 3404747525, 78310609875, 1801154829100, 41426517680375]$ |
$25$ |
$[25, 575, 12100, 278875, 6438875, 148055600, 3404747525, 78310609875, 1801154829100, 41426517680375]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$C_2$ |
simple |
| 1.23.c |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 2 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$26$ |
$[26, 572, 12038, 279136, 6440746, 148043324, 3404709334, 78311046528, 1801155209594, 41426504708732]$ |
$26$ |
$[26, 572, 12038, 279136, 6440746, 148043324, 3404709334, 78311046528, 1801155209594, 41426504708732]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-22}) \) |
$C_2$ |
simple |
| 1.23.d |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 3 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$27$ |
$[27, 567, 11988, 279531, 6441417, 148027824, 3404732967, 78311448243, 1801153399644, 41426498351007]$ |
$27$ |
$[27, 567, 11988, 279531, 6441417, 148027824, 3404732967, 78311448243, 1801153399644, 41426498351007]$ |
$3$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-83}) \) |
$C_2$ |
simple |
| 1.23.e |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 4 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$28$ |
$[28, 560, 11956, 280000, 6440588, 148015280, 3404810276, 78311520000, 1801150871548, 41426506074800]$ |
$28$ |
$[28, 560, 11956, 280000, 6440588, 148015280, 3404810276, 78311520000, 1801150871548, 41426506074800]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \) |
$C_2$ |
simple |
| 1.23.f |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 5 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$29$ |
$[29, 551, 11948, 280459, 6438319, 148011824, 3404900353, 78311164275, 1801150043684, 41426520185711]$ |
$29$ |
$[29, 551, 11948, 280459, 6438319, 148011824, 3404900353, 78311164275, 1801150043684, 41426520185711]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-67}) \) |
$C_2$ |
simple |
| 1.23.g |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 6 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$30$ |
$[30, 540, 11970, 280800, 6435150, 148021020, 3404942130, 78310627200, 1801152126270, 41426522660700]$ |
$30$ |
$[30, 540, 11970, 280800, 6435150, 148021020, 3404942130, 78310627200, 1801152126270, 41426522660700]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-14}) \) |
$C_2$ |
simple |
| 1.23.h |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 7 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$31$ |
$[31, 527, 12028, 280891, 6432221, 148040624, 3404887139, 78310444563, 1801155027604, 41426507087207]$ |
$31$ |
$[31, 527, 12028, 280891, 6432221, 148040624, 3404887139, 78310444563, 1801155027604, 41426507087207]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
simple |
| 1.23.i |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 8 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$32$ |
$[32, 512, 12128, 280576, 6431392, 148058624, 3404757472, 78311006208, 1801154057504, 41426499564032]$ |
$32$ |
$[32, 512, 12128, 280576, 6431392, 148058624, 3404757472, 78311006208, 1801154057504, 41426499564032]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
simple |
| 1.23.j |
$1$ |
$\F_{23}$ |
$23$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 9 x + 23 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$33$ |
$[33, 495, 12276, 279675, 6435363, 148048560, 3404733981, 78311517075, 1801149979068, 41426523123975]$ |
$33$ |
$[33, 495, 12276, 279675, 6435363, 148048560, 3404733981, 78311517075, 1801149979068, 41426523123975]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
simple |
