| 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 |
| 1.19.ai |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 8 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$12$ |
$[12, 336, 6804, 130368, 2477532, 47056464, 893929188, 16983821568, 322688674476, 6131069159376]$ |
$12$ |
$[12, 336, 6804, 130368, 2477532, 47056464, 893929188, 16983821568, 322688674476, 6131069159376]$ |
$2$ |
$2$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.19.ah |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 7 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$13$ |
$[13, 351, 6916, 130923, 2479243, 47056464, 893886097, 16983462483, 322686721084, 6131061331551]$ |
$13$ |
$[13, 351, 6916, 130923, 2479243, 47056464, 893886097, 16983462483, 322686721084, 6131061331551]$ |
$2$ |
$2$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.19.ag |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 6 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$14$ |
$[14, 364, 6986, 131040, 2478014, 47043724, 893822426, 16983308160, 322687105454, 6131067546604]$ |
$14$ |
$[14, 364, 6986, 131040, 2478014, 47043724, 893822426, 16983308160, 322687105454, 6131067546604]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$C_2$ |
simple |
| 1.19.af |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 5 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$15$ |
$[15, 375, 7020, 130875, 2475825, 47034000, 893817555, 16983517875, 322688501460, 6131071134375]$ |
$15$ |
$[15, 375, 7020, 130875, 2475825, 47034000, 893817555, 16983517875, 322688501460, 6131071134375]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-51}) \) |
$C_2$ |
simple |
| 1.19.ae |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 4 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$16$ |
$[16, 384, 7024, 130560, 2473936, 47032704, 893860144, 16983767040, 322688734096, 6131066527104]$ |
$16$ |
$[16, 384, 7024, 130560, 2473936, 47032704, 893860144, 16983767040, 322688734096, 6131066527104]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-15}) \) |
$C_2$ |
simple |
| 1.19.ad |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 3 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$17$ |
$[17, 391, 7004, 130203, 2473007, 47038864, 893909453, 16983809523, 322687720676, 6131061643351]$ |
$17$ |
$[17, 391, 7004, 130203, 2473007, 47038864, 893909453, 16983809523, 322687720676, 6131061643351]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-67}) \) |
$C_2$ |
simple |
| 1.19.ac |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 2 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$18$ |
$[18, 396, 6966, 129888, 2473218, 47048364, 893931462, 16983635328, 322686707634, 6131062904076]$ |
$18$ |
$[18, 396, 6966, 129888, 2473218, 47048364, 893931462, 16983635328, 322686707634, 6131062904076]$ |
$3$ |
$3$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$C_2$ |
simple |
| 1.19.ab |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$19$ |
$[19, 399, 6916, 129675, 2474389, 47056464, 893914831, 16983405075, 322686721084, 6131068282479]$ |
$19$ |
$[19, 399, 6916, 129675, 2474389, 47056464, 893914831, 16983405075, 322686721084, 6131068282479]$ |
$3$ |
$3$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.19.a |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
|
✓ |
✓ |
✓ |
✓ |
$1 + 19 x^{2}$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$1$ |
$0$ |
$1$ |
$0$ |
$1$ |
$20$ |
$[20, 400, 6860, 129600, 2476100, 47059600, 893871740, 16983302400, 322687697780, 6131071210000]$ |
$20$ |
$[20, 400, 6860, 129600, 2476100, 47059600, 893871740, 16983302400, 322687697780, 6131071210000]$ |
$4$ |
$4$ |
$1$ |
$1$ |
$2$ |
\(\Q(\sqrt{-19}) \) |
$C_2$ |
simple |
| 1.19.b |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$21$ |
$[21, 399, 6804, 129675, 2477811, 47056464, 893828649, 16983405075, 322688674476, 6131068282479]$ |
$21$ |
$[21, 399, 6804, 129675, 2477811, 47056464, 893828649, 16983405075, 322688674476, 6131068282479]$ |
$3$ |
$3$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.19.c |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 2 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$22$ |
$[22, 396, 6754, 129888, 2478982, 47048364, 893812018, 16983635328, 322688687926, 6131062904076]$ |
$22$ |
$[22, 396, 6754, 129888, 2478982, 47048364, 893812018, 16983635328, 322688687926, 6131062904076]$ |
$3$ |
$3$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-2}) \) |
$C_2$ |
simple |
| 1.19.d |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 3 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$23$ |
$[23, 391, 6716, 130203, 2479193, 47038864, 893834027, 16983809523, 322687674884, 6131061643351]$ |
$23$ |
$[23, 391, 6716, 130203, 2479193, 47038864, 893834027, 16983809523, 322687674884, 6131061643351]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-67}) \) |
$C_2$ |
simple |
| 1.19.e |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 4 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$24$ |
$[24, 384, 6696, 130560, 2478264, 47032704, 893883336, 16983767040, 322686661464, 6131066527104]$ |
$24$ |
$[24, 384, 6696, 130560, 2478264, 47032704, 893883336, 16983767040, 322686661464, 6131066527104]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-15}) \) |
$C_2$ |
simple |
| 1.19.f |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 5 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$25$ |
$[25, 375, 6700, 130875, 2476375, 47034000, 893925925, 16983517875, 322686894100, 6131071134375]$ |
$25$ |
$[25, 375, 6700, 130875, 2476375, 47034000, 893925925, 16983517875, 322686894100, 6131071134375]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-51}) \) |
$C_2$ |
simple |
| 1.19.g |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 6 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$26$ |
$[26, 364, 6734, 131040, 2474186, 47043724, 893921054, 16983308160, 322688290106, 6131067546604]$ |
$26$ |
$[26, 364, 6734, 131040, 2474186, 47043724, 893921054, 16983308160, 322688290106, 6131067546604]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$C_2$ |
simple |
| 1.19.h |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 7 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$27$ |
$[27, 351, 6804, 130923, 2472957, 47056464, 893857383, 16983462483, 322688674476, 6131061331551]$ |
$27$ |
$[27, 351, 6804, 130923, 2472957, 47056464, 893857383, 16983462483, 322688674476, 6131061331551]$ |
$2$ |
$2$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 1.19.i |
$1$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 + 8 x + 19 x^{2}$ |
$[0,1]$ |
$0$ |
$1$ |
$0$ |
$1$ |
$0$ |
$28$ |
$[28, 336, 6916, 130368, 2474668, 47056464, 893814292, 16983821568, 322686721084, 6131069159376]$ |
$28$ |
$[28, 336, 6916, 130368, 2474668, 47056464, 893814292, 16983821568, 322686721084, 6131069159376]$ |
$2$ |
$2$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
simple |
| 2.19.aq_dy |
$2$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 19 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$4$ |
$[4, 310, 6748, 130414, 2478964, 47067046, 893986636, 16984080094, 322689651172, 6131072060950]$ |
$144$ |
$[144, 112896, 46294416, 16995815424, 6138164811024, 2214310804183296, 799109393158339344, 288450195053661978624, 104127980635077893874576, 37590009037051531288709376]$ |
$1$ |
$1$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
1.19.ai 2 |
| 2.19.ap_dp |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 93 x^{2} - 285 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$5$ |
$[5, 323, 6815, 130443, 2476400, 47040383, 893812085, 16983221443, 322686446195, 6131064236198]$ |
$155$ |
$[155, 117025, 46735445, 16999168525, 6131808122000, 2213056283091025, 798953364541302545, 288435612056346033525, 104126946427712916323255, 37589961062970636364000000]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.1525.1 |
$D_{4}$ |
simple |
| 2.19.ap_dq |
$2$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 19 x^{2} )( 1 - 7 x + 19 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$5$ |
$[5, 325, 6860, 130969, 2480675, 47067046, 893943545, 16983721009, 322687697780, 6131064233125]$ |
$156$ |
$[156, 117936, 47056464, 17068169664, 6142403868276, 2214310804183296, 799070872855699236, 288444096418094233344, 104127350297602681851984, 37589961044115088796272176]$ |
$0$ |
$0$ |
$24$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.19.ai $\times$ 1.19.ah |
| 2.19.ao_dh |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 85 x^{2} - 266 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 336, 6888, 130644, 2476366, 47039070, 893829306, 16983502500, 322688549064, 6131074493536]$ |
$167$ |
$[167, 121409, 47234948, 17025548297, 6131729053647, 2212994534939024, 798968756034428951, 288440385356155507913, 104127624997453294352996, 37590023951405955004876209]$ |
$1$ |
$1$ |
$2$ |
$2$ |
$1$ |
4.0.14912.2 |
$D_{4}$ |
simple |
| 2.19.ao_di |
$2$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 19 x^{2} )( 1 - 6 x + 19 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$6$ |
$[6, 338, 6930, 131086, 2479446, 47054306, 893879874, 16983566686, 322688082150, 6131070448178]$ |
$168$ |
$[168, 122304, 47532744, 17083422720, 6139358981448, 2213711304831936, 799013955490370088, 288441475423798394880, 104127474329448490192104, 37589999149034860983559104]$ |
$4$ |
$4$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-10}) \) |
$C_2$, $C_2$ |
1.19.ai $\times$ 1.19.ag |
| 2.19.ao_dj |
$2$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 19 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$6$ |
$[6, 340, 6972, 131524, 2482386, 47067046, 893900454, 16983361924, 322685744388, 6131056405300]$ |
$169$ |
$[169, 123201, 47831056, 17140831929, 6146645853049, 2214310804183296, 799032354409893409, 288437997911468525289, 104126719963943210135056, 37589913051239921148065601]$ |
$2$ |
$2$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
1.19.ah 2 |
| 2.19.an_cy |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 - 13 x + 76 x^{2} - 247 x^{3} + 361 x^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$2$ |
$0$ |
$7$ |
$[7, 345, 6886, 130185, 2472837, 47026434, 893823679, 16983659793, 322688982466, 6131070755305]$ |
$178$ |
$[178, 124244, 47214856, 16965766688, 6122994315838, 2212400143668416, 798963727685986222, 288443056776740398208, 104127764851098169084072, 37590001032051721372609044]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.43928.1 |
$D_{4}$ |
simple |
| 2.19.an_cz |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 13 x + 77 x^{2} - 247 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 347, 6925, 130555, 2475112, 47036567, 893860807, 16983810019, 322689806185, 6131075312102]$ |
$179$ |
$[179, 125121, 47489237, 17014078701, 6128624886224, 2212876729285569, 798996913370243249, 288445608159578024949, 104128030656023260494527, 37590028970091756735864576]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.64389.1 |
$D_{4}$ |
simple |
| 2.19.an_da |
$2$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 349, 6964, 130921, 2477257, 47044582, 893875003, 16983776401, 322689478156, 6131074035949]$ |
$180$ |
$[180, 126000, 47764080, 17061912000, 6133935663900, 2213253727776000, 799009601161295340, 288445037185938528000, 104127924804774190734960, 37590021145906989987150000]$ |
$4$ |
$4$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-51}) \) |
$C_2$, $C_2$ |
1.19.ai $\times$ 1.19.af |
| 2.19.an_db |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 13 x + 79 x^{2} - 247 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 351, 7003, 131283, 2479272, 47050491, 893866813, 16983571443, 322688189557, 6131069106406]$ |
$181$ |
$[181, 126881, 48039391, 17109268445, 6138926902096, 2213531724084521, 799002280193961451, 288441556256912702645, 104127508988997935788441, 37589990922529927848066816]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.21125.1 |
$C_4$ |
simple |
| 2.19.an_dc |
$2$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 7 x + 19 x^{2} )( 1 - 6 x + 19 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$7$ |
$[7, 353, 7042, 131641, 2481157, 47054306, 893836783, 16983207601, 322686128758, 6131062620353]$ |
$182$ |
$[182, 127764, 48315176, 17156149920, 6143598863402, 2213711304831936, 798975439788211322, 288435376972587761280, 104126843995038193192136, 37589951156111042988102804]$ |
$0$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-10}) \) |
$C_2$, $C_2$ |
1.19.ah $\times$ 1.19.ag |
| 2.19.am_cp |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 12 x + 67 x^{2} - 228 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$8$ |
$[8, 352, 6860, 129700, 2470688, 47026222, 893856608, 16983689284, 322687697780, 6131061446752]$ |
$189$ |
$[189, 126441, 47036052, 16902759321, 6117677843949, 2212390187746704, 798993160685911989, 288443557605540195369, 104127350298348762476532, 37589943960696653730888201]$ |
$4$ |
$4$ |
$4$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{7})\) |
$C_2^2$ |
simple |
| 2.19.am_cq |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 12 x + 68 x^{2} - 228 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 354, 6896, 130006, 2472368, 47033682, 893894072, 16983923806, 322689074024, 6131067736674]$ |
$190$ |
$[190, 127300, 47287390, 16942611600, 6121833155950, 2212741065343300, 799026649637951470, 288447540686741606400, 104127794396037832168030, 37589982524610807362282500]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.168192.4 |
$D_{4}$ |
simple |
| 2.19.am_cr |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 12 x + 69 x^{2} - 228 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 356, 6932, 130308, 2473928, 47039366, 893914232, 16984032388, 322689696428, 6131069897156]$ |
$191$ |
$[191, 128161, 47539136, 16981973305, 6125692347071, 2213008391520256, 799044670009668791, 288449384824034140905, 104127995238661094476736, 37589995770672827115745441]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.12625.1 |
$D_{4}$ |
simple |
| 2.19.am_cs |
$2$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 19 x^{2} )( 1 - 4 x + 19 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 358, 6968, 130606, 2475368, 47043286, 893917592, 16984025566, 322689710792, 6131069428678]$ |
$192$ |
$[192, 129024, 47791296, 17020846080, 6129255605952, 2213192742598656, 799047672711483072, 288449268959839518720, 104127999873776666133696, 37589992898409852999727104]$ |
$12$ |
$12$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) |
$C_2$, $C_2$ |
1.19.ai $\times$ 1.19.ae |
| 2.19.am_ct |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 12 x + 71 x^{2} - 228 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 360, 7004, 130900, 2476688, 47045454, 893904656, 16983913828, 322689260324, 6131067761880]$ |
$193$ |
$[193, 129889, 48043876, 17059231593, 6132523129513, 2213294696167696, 799036108767783457, 288447371227918952073, 104127854512771789161412, 37589982679159238495800369]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.134928.2 |
$D_{4}$ |
simple |
| 2.19.am_cu |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 12 x + 72 x^{2} - 228 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$8$ |
$[8, 362, 7040, 131190, 2477888, 47045882, 893875928, 16983707614, 322688485640, 6131066257802]$ |
$194$ |
$[194, 130756, 48296882, 17097131536, 6135495123074, 2213314831134724, 799010429326500914, 288443868954489667584, 104127604530951176173442, 37589973457544943538923076]$ |
$5$ |
$5$ |
$8$ |
$24$ |
$4$ |
\(\Q(\zeta_{8})\) |
$C_2^2$ |
simple |
| 2.19.am_cv |
$2$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$8$ |
$[8, 364, 7076, 131476, 2478968, 47044582, 893831912, 16983417316, 322687524764, 6131066208124]$ |
$195$ |
$[195, 131625, 48550320, 17134547625, 6138171800475, 2213253727776000, 798971085669032835, 288438938659422383625, 104127294467636946782640, 37589973152955087548165625]$ |
$8$ |
$8$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-51}) \) |
$C_2$, $C_2$ |
1.19.ah $\times$ 1.19.af |
| 2.19.am_cw |
$2$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 6 x + 19 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$8$ |
$[8, 366, 7112, 131758, 2479928, 47041566, 893773112, 16983053278, 322686513128, 6131068835406]$ |
$196$ |
$[196, 132496, 48804196, 17171481600, 6140553384196, 2213111967788176, 798918529220525476, 288432756057522585600, 104126968026280916546116, 37589989261020791711932816]$ |
$4$ |
$4$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-10}) \) |
$C_2$ |
1.19.ag 2 |
| 2.19.al_cg |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 58 x^{2} - 209 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 357, 6816, 129273, 2470039, 47032662, 893874501, 16983472113, 322685962464, 6131057792677]$ |
$200$ |
$[200, 128000, 46738400, 16847360000, 6116072751000, 2212693071872000, 799009152438764600, 288439869271132160000, 104126790334174227960800, 37589921557333848835200000]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.8405.1 |
$D_{4}$ |
simple |
| 2.19.al_ch |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 59 x^{2} - 209 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 359, 6849, 129523, 2471304, 47039051, 893916543, 16983744979, 322687359387, 6131063631014]$ |
$201$ |
$[201, 128841, 46967067, 16879845933, 6119201069616, 2212993652334129, 799046735188015263, 288444503541941961237, 104127241103131388139333, 37589957352536821973926656]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.291597.2 |
$D_{4}$ |
simple |
| 2.19.al_ci |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 60 x^{2} - 209 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 361, 6882, 129769, 2472459, 47043970, 893945649, 16983929425, 322688208246, 6131066027161]$ |
$202$ |
$[202, 129684, 47196088, 16911831072, 6122057290822, 2213225055301824, 799072753925610646, 288447636123620162688, 104127515019253716936856, 37589972043459737592720084]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.444312.2 |
$D_{4}$ |
simple |
| 2.19.al_cj |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 61 x^{2} - 209 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 363, 6915, 130011, 2473504, 47047431, 893962281, 16984034211, 322688618535, 6131066008678]$ |
$203$ |
$[203, 130529, 47425469, 16943316845, 6124641547248, 2213387850962561, 799087621661019593, 288449415785418438005, 104127647414623118474279, 37589971930139626308751104]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.508805.3 |
$D_{4}$ |
simple |
| 2.19.al_ck |
$2$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 19 x^{2} )( 1 - 3 x + 19 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 365, 6948, 130249, 2474439, 47049446, 893966901, 16984068049, 322688697372, 6131064544925]$ |
$204$ |
$[204, 131376, 47655216, 16974304704, 6126953978724, 2213482610416896, 799091751465814164, 288449990483531192064, 104127672854620178665776, 37589962955782452689708976]$ |
$4$ |
$4$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-67}) \) |
$C_2$, $C_2$ |
1.19.ai $\times$ 1.19.ad |
| 2.19.al_cl |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 63 x^{2} - 209 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 367, 6981, 130483, 2475264, 47050027, 893959971, 16984039603, 322688549499, 6131062547302]$ |
$205$ |
$[205, 132225, 47885335, 17004796125, 6128994732400, 2213509905722025, 799085556480660115, 288449507361741091125, 104127625137960514438945, 37589950708235677119840000]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.443205.2 |
$D_{4}$ |
simple |
| 2.19.al_cm |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 64 x^{2} - 209 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 369, 7014, 130713, 2475979, 47049186, 893941953, 16983957489, 322688277282, 6131060869489]$ |
$206$ |
$[206, 133076, 48115832, 17034792608, 6130763962866, 2213470309936064, 799069449922614818, 288448112752124296832, 104127537296738062291928, 37589940421461346132563156]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.349112.1 |
$D_{4}$ |
simple |
| 2.19.al_cn |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 65 x^{2} - 209 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 371, 7047, 130939, 2476584, 47046935, 893913309, 16983830275, 322687980711, 6131060307686]$ |
$207$ |
$[207, 133929, 48346713, 17064295677, 6132261832272, 2213364397163049, 799043845092737661, 288445952175817883733, 104127441596475871887171, 37589936977009790399856384]$ |
$5$ |
$5$ |
$2$ |
$2$ |
$1$ |
4.0.26533.1 |
$D_{4}$ |
simple |
| 2.19.al_co |
$2$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 7 x + 19 x^{2} )( 1 - 4 x + 19 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 373, 7080, 131161, 2477079, 47043286, 893874501, 16983666481, 322687757400, 6131061600853]$ |
$208$ |
$[208, 134784, 48577984, 17093306880, 6133488510448, 2213192742598656, 799009155384017968, 288443170343851960320, 104127369536184992880064, 37589944905494015471858304]$ |
$6$ |
$6$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) |
$C_2$, $C_2$ |
1.19.ah $\times$ 1.19.ae |
| 2.19.al_cp |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 11 x + 67 x^{2} - 209 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 375, 7113, 131379, 2477464, 47038251, 893825991, 16983474579, 322687702587, 6131065430950]$ |
$209$ |
$[209, 135641, 48809651, 17121827789, 6134444175024, 2212955922576641, 798965794289625479, 288439911158049053909, 104127351848432066042141, 37589968388064876490181376]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.45725.1 |
$D_{4}$ |
simple |
| 2.19.al_cq |
$2$ |
$\F_{19}$ |
$19$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 6 x + 19 x^{2} )( 1 - 5 x + 19 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$9$ |
$[9, 377, 7146, 131593, 2477739, 47031842, 893768241, 16983262993, 322687909134, 6131072423177]$ |
$210$ |
$[210, 136500, 49041720, 17149860000, 6135129011550, 2212654514616000, 798914175411488430, 288436317711993360000, 104127418499416252962840, 37590011257887134458912500]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-51}) \) |
$C_2$, $C_2$ |
1.19.ag $\times$ 1.19.af |
| 2.19.ak_by |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 50 x^{2} - 190 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$10$ |
$[10, 362, 6790, 129166, 2471650, 47045882, 893899870, 16983416158, 322686428890, 6131066257802]$ |
$212$ |
$[212, 129744, 46568132, 16833505536, 6120057514052, 2213314951942224, 799031830790578772, 288438918993308160000, 104126940843523446384692, 37589973457558189176538704]$ |
$8$ |
$8$ |
$4$ |
$8$ |
$4$ |
\(\Q(i, \sqrt{13})\) |
$C_2^2$ |
simple |
| 2.19.ak_bz |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 51 x^{2} - 190 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$10$ |
$[10, 364, 6820, 129364, 2472550, 47050918, 893935570, 16983615844, 322687208860, 6131068985404]$ |
$213$ |
$[213, 130569, 46774800, 16859199849, 6122283767853, 2213551925280000, 799063743815563173, 288442310363975783049, 104127192529352677789200, 37589990180663150170659609]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.46224.1 |
$D_{4}$ |
simple |
| 2.19.ak_ca |
$2$ |
$\F_{19}$ |
$19$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 10 x + 52 x^{2} - 190 x^{3} + 361 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$10$ |
$[10, 366, 6850, 129558, 2473350, 47054766, 893962030, 16983757278, 322687625770, 6131069385406]$ |
$214$ |
$[214, 131396, 46981774, 16884386000, 6124262327854, 2213732987579876, 799087397110427254, 288444712420098176000, 104127327060645758306374, 37589992633096691075945316]$ |
$10$ |
$10$ |
$2$ |
$2$ |
$1$ |
4.0.38720.3 |
$D_{4}$ |
simple |
