| 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 |
| 1.37.am |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 12 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$26$ |
$[26, 1300, 50258, 1872000, 69332666, 2565670900, 94931628818, 3512478528000, 129961737871706, 4808584383596500]$ |
$26$ |
$[26, 1300, 50258, 1872000, 69332666, 2565670900, 94931628818, 3512478528000, 129961737871706, 4808584383596500]$ |
$1$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
| 1.37.al |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$27$ |
$[27, 1323, 50544, 1874691, 69353847, 2565815616, 94932492507, 3512482922403, 129961755179568, 4808584413313443]$ |
$27$ |
$[27, 1323, 50544, 1874691, 69353847, 2565815616, 94932492507, 3512482922403, 129961755179568, 4808584413313443]$ |
$2$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.37.ak |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$28$ |
$[28, 1344, 50764, 1876224, 69360508, 2565815616, 94932156844, 3512478950400, 129961724410588, 4808584237203264]$ |
$28$ |
$[28, 1344, 50764, 1876224, 69360508, 2565815616, 94932156844, 3512478950400, 129961724410588, 4808584237203264]$ |
$4$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.37.aj |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 9 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$29$ |
$[29, 1363, 50924, 1876851, 69358169, 2565754816, 94931606981, 3512475971523, 129961718449148, 4808584309153243]$ |
$29$ |
$[29, 1363, 50924, 1876851, 69358169, 2565754816, 94931606981, 3512475971523, 129961718449148, 4808584309153243]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-67}) \) |
$C_2$ |
simple |
| 1.37.ai |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$30$ |
$[30, 1380, 51030, 1876800, 69351150, 2565686340, 94931290470, 3512476243200, 129961735815870, 4808584459380900]$ |
$30$ |
$[30, 1380, 51030, 1876800, 69351150, 2565686340, 94931290470, 3512476243200, 129961735815870, 4808584459380900]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-21}) \) |
$C_2$ |
simple |
| 1.37.ah |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$31$ |
$[31, 1395, 51088, 1876275, 69342691, 2565639360, 94931314663, 3512478737475, 129961755591376, 4808584509500475]$ |
$31$ |
$[31, 1395, 51088, 1876275, 69342691, 2565639360, 94931314663, 3512478737475, 129961755591376, 4808584509500475]$ |
$3$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
simple |
| 1.37.ag |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 6 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$32$ |
$[32, 1408, 51104, 1875456, 69335072, 2565625216, 94931598752, 3512481527808, 129961762538528, 4808584432144768]$ |
$32$ |
$[32, 1408, 51104, 1875456, 69335072, 2565625216, 94931598752, 3512481527808, 129961762538528, 4808584432144768]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
simple |
| 1.37.af |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 5 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$33$ |
$[33, 1419, 51084, 1874499, 69329733, 2565642816, 94931985489, 3512483088675, 129961753959708, 4808584308755139]$ |
$33$ |
$[33, 1419, 51084, 1874499, 69329733, 2565642816, 94931985489, 3512483088675, 129961753959708, 4808584308755139]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-123}) \) |
$C_2$ |
simple |
| 1.37.ae |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 4 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$34$ |
$[34, 1428, 51034, 1873536, 69327394, 2565683316, 94932317626, 3512482810368, 129961736922658, 4808584236739668]$ |
$34$ |
$[34, 1428, 51034, 1873536, 69327394, 2565683316, 94932317626, 3512482810368, 129961736922658, 4808584236739668]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-33}) \) |
$C_2$ |
simple |
| 1.37.ad |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$35$ |
$[35, 1435, 50960, 1872675, 69328175, 2565734080, 94932484115, 3512480991075, 129961721948240, 4808584262002675]$ |
$35$ |
$[35, 1435, 50960, 1872675, 69328175, 2565734080, 94932484115, 3512480991075, 129961721948240, 4808584262002675]$ |
$3$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-139}) \) |
$C_2$ |
simple |
| 1.37.ac |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$36$ |
$[36, 1440, 50868, 1872000, 69331716, 2565781920, 94932441108, 3512478528000, 129961717076196, 4808584361239200]$ |
$36$ |
$[36, 1440, 50868, 1872000, 69331716, 2565781920, 94932441108, 3512478528000, 129961717076196, 4808584361239200]$ |
$8$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
| 1.37.ab |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$37$ |
$[37, 1443, 50764, 1871571, 69337297, 2565815616, 94932212797, 3512476488963, 129961724410588, 4808584466736843]$ |
$37$ |
$[37, 1443, 50764, 1871571, 69337297, 2565815616, 94932212797, 3512476488963, 129961724410588, 4808584466736843]$ |
$3$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.37.a |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
|
✓ |
✓ |
✓ |
✓ |
$1 + 37 x^{2}$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$1$ |
$0$ |
$1$ |
$0$ |
$1$ |
$38$ |
$[38, 1444, 50654, 1871424, 69343958, 2565827716, 94931877134, 3512475705600, 129961739795078, 4808584511105764]$ |
$38$ |
$[38, 1444, 50654, 1871424, 69343958, 2565827716, 94931877134, 3512475705600, 129961739795078, 4808584511105764]$ |
$2$ |
$0$ |
$1$ |
$1$ |
$2$ |
\(\Q(\sqrt{-37}) \) |
$C_2$ |
simple |
| 1.37.b |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$39$ |
$[39, 1443, 50544, 1871571, 69350619, 2565815616, 94931541471, 3512476488963, 129961755179568, 4808584466736843]$ |
$39$ |
$[39, 1443, 50544, 1871571, 69350619, 2565815616, 94931541471, 3512476488963, 129961755179568, 4808584466736843]$ |
$3$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.37.c |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 2 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$40$ |
$[40, 1440, 50440, 1872000, 69356200, 2565781920, 94931313160, 3512478528000, 129961762513960, 4808584361239200]$ |
$40$ |
$[40, 1440, 50440, 1872000, 69356200, 2565781920, 94931313160, 3512478528000, 129961762513960, 4808584361239200]$ |
$8$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |
| 1.37.d |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 3 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$41$ |
$[41, 1435, 50348, 1872675, 69359741, 2565734080, 94931270153, 3512480991075, 129961757641916, 4808584262002675]$ |
$41$ |
$[41, 1435, 50348, 1872675, 69359741, 2565734080, 94931270153, 3512480991075, 129961757641916, 4808584262002675]$ |
$3$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-139}) \) |
$C_2$ |
simple |
| 1.37.e |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 4 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$42$ |
$[42, 1428, 50274, 1873536, 69360522, 2565683316, 94931436642, 3512482810368, 129961742667498, 4808584236739668]$ |
$42$ |
$[42, 1428, 50274, 1873536, 69360522, 2565683316, 94931436642, 3512482810368, 129961742667498, 4808584236739668]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-33}) \) |
$C_2$ |
simple |
| 1.37.f |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 5 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$43$ |
$[43, 1419, 50224, 1874499, 69358183, 2565642816, 94931768779, 3512483088675, 129961725630448, 4808584308755139]$ |
$43$ |
$[43, 1419, 50224, 1874499, 69358183, 2565642816, 94931768779, 3512483088675, 129961725630448, 4808584308755139]$ |
$2$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-123}) \) |
$C_2$ |
simple |
| 1.37.g |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 6 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$44$ |
$[44, 1408, 50204, 1875456, 69352844, 2565625216, 94932155516, 3512481527808, 129961717051628, 4808584432144768]$ |
$44$ |
$[44, 1408, 50204, 1875456, 69352844, 2565625216, 94932155516, 3512481527808, 129961717051628, 4808584432144768]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-7}) \) |
$C_2$ |
simple |
| 1.37.h |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 7 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$45$ |
$[45, 1395, 50220, 1876275, 69345225, 2565639360, 94932439605, 3512478737475, 129961723998780, 4808584509500475]$ |
$45$ |
$[45, 1395, 50220, 1876275, 69345225, 2565639360, 94932439605, 3512478737475, 129961723998780, 4808584509500475]$ |
$3$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
simple |
| 1.37.i |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 8 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$46$ |
$[46, 1380, 50278, 1876800, 69336766, 2565686340, 94932463798, 3512476243200, 129961743774286, 4808584459380900]$ |
$46$ |
$[46, 1380, 50278, 1876800, 69336766, 2565686340, 94932463798, 3512476243200, 129961743774286, 4808584459380900]$ |
$4$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-21}) \) |
$C_2$ |
simple |
| 1.37.j |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 9 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$47$ |
$[47, 1363, 50384, 1876851, 69329747, 2565754816, 94932147287, 3512475971523, 129961761141008, 4808584309153243]$ |
$47$ |
$[47, 1363, 50384, 1876851, 69329747, 2565754816, 94932147287, 3512475971523, 129961761141008, 4808584309153243]$ |
$1$ |
$0$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-67}) \) |
$C_2$ |
simple |
| 1.37.k |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 10 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$48$ |
$[48, 1344, 50544, 1876224, 69327408, 2565815616, 94931597424, 3512478950400, 129961755179568, 4808584237203264]$ |
$48$ |
$[48, 1344, 50544, 1876224, 69327408, 2565815616, 94931597424, 3512478950400, 129961755179568, 4808584237203264]$ |
$4$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.37.l |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 11 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$49$ |
$[49, 1323, 50764, 1874691, 69334069, 2565815616, 94931261761, 3512482922403, 129961724410588, 4808584413313443]$ |
$49$ |
$[49, 1323, 50764, 1874691, 69334069, 2565815616, 94931261761, 3512482922403, 129961724410588, 4808584413313443]$ |
$2$ |
$0$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.37.m |
$1$ |
$\F_{37}$ |
$37$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 12 x + 37 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$50$ |
$[50, 1300, 51050, 1872000, 69355250, 2565670900, 94932125450, 3512478528000, 129961741718450, 4808584383596500]$ |
$50$ |
$[50, 1300, 51050, 1872000, 69355250, 2565670900, 94932125450, 3512478528000, 129961741718450, 4808584383596500]$ |
$1$ |
$0$ |
$4$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
simple |