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 |
1.53.ao |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$40$ |
$[40, 2720, 148360, 7888000, 418188200, 22164390560, 1174711938440, 62259700032000, 3299763684165160, 174887471148701600]$ |
$40$ |
$[40, 2720, 148360, 7888000, 418188200, 22164390560, 1174711938440, 62259700032000, 3299763684165160, 174887471148701600]$ |
$2$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
1.53.an |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 13 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$41$ |
$[41, 2747, 148748, 7892131, 418223821, 22164641984, 1174713289609, 62259703473123, 3299763647667164, 174887470399485107]$ |
$41$ |
$[41, 2747, 148748, 7892131, 418223821, 22164641984, 1174713289609, 62259703473123, 3299763647667164, 174887470399485107]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
simple |
1.53.am |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 12 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$42$ |
$[42, 2772, 149058, 7894656, 418236042, 22164626484, 1174712175042, 62259688770048, 3299763517240554, 174887469557763732]$ |
$42$ |
$[42, 2772, 149058, 7894656, 418236042, 22164626484, 1174712175042, 62259688770048, 3299763517240554, 174887469557763732]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-17}) \) |
$C_2$ |
simple |
1.53.al |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$43$ |
$[43, 2795, 149296, 7895875, 418232663, 22164484160, 1174710523211, 62259677107875, 3299763478145008, 174887469820369475]$ |
$43$ |
$[43, 2795, 149296, 7895875, 418232663, 22164484160, 1174710523211, 62259677107875, 3299763478145008, 174887469820369475]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$C_2$ |
simple |
1.53.ak |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$44$ |
$[44, 2816, 149468, 7896064, 418220044, 22164310784, 1174709335228, 62259675033600, 3299763533668844, 174887470599201536]$ |
$44$ |
$[44, 2816, 149468, 7896064, 418220044, 22164310784, 1174709335228, 62259675033600, 3299763533668844, 174887470599201536]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
simple |
1.53.aj |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$45$ |
$[45, 2835, 149580, 7895475, 418203225, 22164166080, 1174708974645, 62259681262275, 3299763624215580, 174887471142135675]$ |
$45$ |
$[45, 2835, 149580, 7895475, 418203225, 22164166080, 1174708974645, 62259681262275, 3299763624215580, 174887471142135675]$ |
$5$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-131}) \) |
$C_2$ |
simple |
1.53.ai |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$46$ |
$[46, 2852, 149638, 7894336, 418186046, 22164081284, 1174709401814, 62259691339008, 3299763691338574, 174887471112639332]$ |
$46$ |
$[46, 2852, 149638, 7894336, 418186046, 22164081284, 1174709401814, 62259691339008, 3299763691338574, 174887471112639332]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-37}) \) |
$C_2$ |
simple |
1.53.ah |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$47$ |
$[47, 2867, 149648, 7892851, 418171267, 22164065984, 1174710357847, 62259700580163, 3299763704429264, 174887470614956507]$ |
$47$ |
$[47, 2867, 149648, 7892851, 418171267, 22164065984, 1174710357847, 62259700580163, 3299763704429264, 174887470614956507]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-163}) \) |
$C_2$ |
simple |
1.53.ag |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 6 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$48$ |
$[48, 2880, 149616, 7891200, 418160688, 22164114240, 1174711503216, 62259705676800, 3299763664135728, 174887469990446400]$ |
$48$ |
$[48, 2880, 149616, 7891200, 418160688, 22164114240, 1174711503216, 62259705676800, 3299763664135728, 174887469990446400]$ |
$10$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
simple |
1.53.af |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 5 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$49$ |
$[49, 2891, 149548, 7889539, 418155269, 22164209984, 1174712516033, 62259705303075, 3299763593322364, 174887469583853411]$ |
$49$ |
$[49, 2891, 149548, 7889539, 418155269, 22164209984, 1174712516033, 62259705303075, 3299763593322364, 174887469583853411]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-187}) \) |
$C_2$ |
simple |
1.53.ae |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 4 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$50$ |
$[50, 2900, 149450, 7888000, 418155250, 22164331700, 1174713155050, 62259700032000, 3299763523478450, 174887469582324500]$ |
$50$ |
$[50, 2900, 149450, 7888000, 418155250, 22164331700, 1174713155050, 62259700032000, 3299763523478450, 174887469582324500]$ |
$5$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
1.53.ad |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$51$ |
$[51, 2907, 149328, 7886691, 418160271, 22164456384, 1174713292419, 62259691820643, 3299763481943184, 174887469961244307]$ |
$51$ |
$[51, 2907, 149328, 7886691, 418160271, 22164456384, 1174713292419, 62259691820643, 3299763481943184, 174887469961244307]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-203}) \) |
$C_2$ |
simple |
1.53.ac |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$52$ |
$[52, 2912, 149188, 7885696, 418169492, 22164562784, 1174712921252, 62259683286528, 3299763483137524, 174887470525800032]$ |
$52$ |
$[52, 2912, 149188, 7885696, 418169492, 22164562784, 1174712921252, 62259683286528, 3299763483137524, 174887470525800032]$ |
$6$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-13}) \) |
$C_2$ |
simple |
1.53.ab |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$53$ |
$[53, 2915, 149036, 7885075, 418181713, 22164633920, 1174712143021, 62259676956675, 3299763525178748, 174887471011988075]$ |
$53$ |
$[53, 2915, 149036, 7885075, 418181713, 22164633920, 1174712143021, 62259676956675, 3299763525178748, 174887471011988075]$ |
$3$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-211}) \) |
$C_2$ |
simple |
1.53.a |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
|
✓ |
✓ |
✓ |
✓ |
$1 + 53 x^{2}$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$1$ |
$0$ |
$1$ |
$0$ |
$1$ |
$54$ |
$[54, 2916, 148878, 7884864, 418195494, 22164658884, 1174711139838, 62259674630400, 3299763591802134, 174887471201904036]$ |
$54$ |
$[54, 2916, 148878, 7884864, 418195494, 22164658884, 1174711139838, 62259674630400, 3299763591802134, 174887471201904036]$ |
$6$ |
$0$ |
$1$ |
$1$ |
$2$ |
\(\Q(\sqrt{-53}) \) |
$C_2$ |
simple |
1.53.b |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$55$ |
$[55, 2915, 148720, 7885075, 418209275, 22164633920, 1174710136655, 62259676956675, 3299763658425520, 174887471011988075]$ |
$55$ |
$[55, 2915, 148720, 7885075, 418209275, 22164633920, 1174710136655, 62259676956675, 3299763658425520, 174887471011988075]$ |
$3$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-211}) \) |
$C_2$ |
simple |
1.53.c |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 2 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$56$ |
$[56, 2912, 148568, 7885696, 418221496, 22164562784, 1174709358424, 62259683286528, 3299763700466744, 174887470525800032]$ |
$56$ |
$[56, 2912, 148568, 7885696, 418221496, 22164562784, 1174709358424, 62259683286528, 3299763700466744, 174887470525800032]$ |
$6$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-13}) \) |
$C_2$ |
simple |
1.53.d |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 3 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$57$ |
$[57, 2907, 148428, 7886691, 418230717, 22164456384, 1174708987257, 62259691820643, 3299763701661084, 174887469961244307]$ |
$57$ |
$[57, 2907, 148428, 7886691, 418230717, 22164456384, 1174708987257, 62259691820643, 3299763701661084, 174887469961244307]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-203}) \) |
$C_2$ |
simple |
1.53.e |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 4 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$58$ |
$[58, 2900, 148306, 7888000, 418235738, 22164331700, 1174709124626, 62259700032000, 3299763660125818, 174887469582324500]$ |
$58$ |
$[58, 2900, 148306, 7888000, 418235738, 22164331700, 1174709124626, 62259700032000, 3299763660125818, 174887469582324500]$ |
$5$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
1.53.f |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 5 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$59$ |
$[59, 2891, 148208, 7889539, 418235719, 22164209984, 1174709763643, 62259705303075, 3299763590281904, 174887469583853411]$ |
$59$ |
$[59, 2891, 148208, 7889539, 418235719, 22164209984, 1174709763643, 62259705303075, 3299763590281904, 174887469583853411]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-187}) \) |
$C_2$ |
simple |
1.53.g |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 6 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$60$ |
$[60, 2880, 148140, 7891200, 418230300, 22164114240, 1174710776460, 62259705676800, 3299763519468540, 174887469990446400]$ |
$60$ |
$[60, 2880, 148140, 7891200, 418230300, 22164114240, 1174710776460, 62259705676800, 3299763519468540, 174887469990446400]$ |
$10$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
simple |
1.53.h |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 7 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$61$ |
$[61, 2867, 148108, 7892851, 418219721, 22164065984, 1174711921829, 62259700580163, 3299763479175004, 174887470614956507]$ |
$61$ |
$[61, 2867, 148108, 7892851, 418219721, 22164065984, 1174711921829, 62259700580163, 3299763479175004, 174887470614956507]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-163}) \) |
$C_2$ |
simple |
1.53.i |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 8 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$62$ |
$[62, 2852, 148118, 7894336, 418204942, 22164081284, 1174712877862, 62259691339008, 3299763492265694, 174887471112639332]$ |
$62$ |
$[62, 2852, 148118, 7894336, 418204942, 22164081284, 1174712877862, 62259691339008, 3299763492265694, 174887471112639332]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-37}) \) |
$C_2$ |
simple |
1.53.j |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 9 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$63$ |
$[63, 2835, 148176, 7895475, 418187763, 22164166080, 1174713305031, 62259681262275, 3299763559388688, 174887471142135675]$ |
$63$ |
$[63, 2835, 148176, 7895475, 418187763, 22164166080, 1174713305031, 62259681262275, 3299763559388688, 174887471142135675]$ |
$5$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-131}) \) |
$C_2$ |
simple |
1.53.k |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 10 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$64$ |
$[64, 2816, 148288, 7896064, 418170944, 22164310784, 1174712944448, 62259675033600, 3299763649935424, 174887470599201536]$ |
$64$ |
$[64, 2816, 148288, 7896064, 418170944, 22164310784, 1174712944448, 62259675033600, 3299763649935424, 174887470599201536]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
simple |
1.53.l |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 11 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$65$ |
$[65, 2795, 148460, 7895875, 418158325, 22164484160, 1174711756465, 62259677107875, 3299763705459260, 174887469820369475]$ |
$65$ |
$[65, 2795, 148460, 7895875, 418158325, 22164484160, 1174711756465, 62259677107875, 3299763705459260, 174887469820369475]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$C_2$ |
simple |
1.53.m |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 12 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$66$ |
$[66, 2772, 148698, 7894656, 418154946, 22164626484, 1174710104634, 62259688770048, 3299763666363714, 174887469557763732]$ |
$66$ |
$[66, 2772, 148698, 7894656, 418154946, 22164626484, 1174710104634, 62259688770048, 3299763666363714, 174887469557763732]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-17}) \) |
$C_2$ |
simple |
1.53.n |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 13 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$67$ |
$[67, 2747, 149008, 7892131, 418167167, 22164641984, 1174708990067, 62259703473123, 3299763535937104, 174887470399485107]$ |
$67$ |
$[67, 2747, 149008, 7892131, 418167167, 22164641984, 1174708990067, 62259703473123, 3299763535937104, 174887470399485107]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
simple |
1.53.o |
$1$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 14 x + 53 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$68$ |
$[68, 2720, 149396, 7888000, 418202788, 22164390560, 1174710341236, 62259700032000, 3299763499439108, 174887471148701600]$ |
$68$ |
$[68, 2720, 149396, 7888000, 418202788, 22164390560, 1174710341236, 62259700032000, 3299763499439108, 174887471148701600]$ |
$2$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |