| 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 |
| 3.5.am_cl_ahc |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-6$ |
$[-6, 8, 114, 668, 3354, 16328, 79794, 393788, 1957434, 9767048]$ |
$8$ |
$[8, 8000, 1815848, 262144000, 32829478408, 3989418056000, 487109020230568, 60088890949632000, 7467037859231032328, 931458479815781000000]$ |
$0$ |
$0$ |
$44$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.5.ae 3 |
| 3.5.al_cd_agc |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-5$ |
$[-5, 15, 136, 703, 3335, 16020, 78731, 391583, 1955080, 9769575]$ |
$12$ |
$[12, 10800, 2143296, 276480000, 32634675132, 3911943859200, 480528139107756, 59750614794240000, 7458044843342751552, 931699496759954670000]$ |
$0$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.5.ae 2 $\times$ 1.5.ad |
| 3.5.ak_bu_aey |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-4$ |
$[-4, 18, 122, 594, 3016, 15576, 78760, 392546, 1954562, 9760818]$ |
$14$ |
$[14, 11060, 1889048, 232525440, 29454708094, 3802502500160, 480722597657974, 59898264082352640, 7456069730475878456, 930864295916013437300]$ |
$0$ |
$0$ |
$24$ |
$24$ |
$6$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{2}, \sqrt{-3})\) |
$C_2$, $C_2^2$ |
1.5.ae $\times$ 2.5.ag_r |
| 3.5.ak_bv_afc |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-4$ |
$[-4, 20, 140, 668, 3196, 15860, 79180, 393788, 1958396, 9766100]$ |
$16$ |
$[16, 12800, 2202832, 262144000, 31209535376, 3871697523200, 483307833956432, 60088890949632000, 7470712999963626256, 931368062695449920000]$ |
$0$ |
$0$ |
$44$ |
$12$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.5.ae 2 $\times$ 1.5.ac |
| 3.5.ak_bw_afg |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-4$ |
$[-4, 22, 158, 738, 3316, 15712, 77668, 389378, 1952726, 9772102]$ |
$18$ |
$[18, 14580, 2529792, 291600000, 32441027778, 3835974205440, 474036166205802, 59414242996800000, 7449062658300154368, 931940576067796326900]$ |
$0$ |
$0$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.5.ae $\times$ 1.5.ad 2 |
| 3.5.aj_bm_ady |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-3$ |
$[-3, 21, 117, 577, 3102, 16029, 79377, 392033, 1954017, 9771936]$ |
$18$ |
$[18, 12420, 1841346, 226143360, 30293942688, 3914499047940, 484529091662466, 59819826030912000, 7453977476504082498, 931924658250690969600]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-9 +2 \sqrt{13}})\) |
$C_2$, $D_{4}$ |
1.5.ae $\times$ 2.5.af_n |
| 3.5.aj_bn_aec |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-3$ |
$[-3, 23, 132, 623, 3177, 16148, 79797, 393023, 1953492, 9762623]$ |
$20$ |
$[20, 14000, 2083760, 243712000, 31014732100, 3944140928000, 487127592801940, 59971529834496000, 7451978186915143280, 931036437877526750000]$ |
$0$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.5.ae 2 $\times$ 1.5.ab |
| 3.5.aj_bo_aeh |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-3$ |
$[-3, 25, 144, 629, 2997, 15268, 77697, 390341, 1952208, 9763345]$ |
$21$ |
$[21, 14931, 2229696, 245241675, 29279930001, 3728658189312, 474227997605733, 59561061079131675, 7447089924183962304, 931105159113787345611]$ |
$0$ |
$0$ |
$12$ |
$24$ |
$6$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{2}, \sqrt{-3})\) |
$C_2$, $C_2^2$ |
1.5.ad $\times$ 2.5.ag_r |
| 3.5.aj_bo_aeg |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$1$ |
$2$ |
$-3$ |
$[-3, 25, 147, 665, 3202, 15985, 79307, 392305, 1951437, 9753600]$ |
$22$ |
$[22, 15620, 2336422, 260416640, 31249521952, 3903296685860, 484097201286182, 59861403245191680, 7444144063593167062, 930176295376956953600]$ |
$0$ |
$0$ |
$28$ |
$60$ |
$10$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{5})\) |
$C_2$, $C_4$ |
1.5.ae $\times$ 2.5.af_p |
| 3.5.aj_bp_aek |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-3$ |
$[-3, 27, 162, 703, 3177, 15552, 78117, 391583, 1956042, 9768627]$ |
$24$ |
$[24, 17280, 2600064, 276480000, 31024344504, 3796509450240, 476778307158744, 59750614794240000, 7461715557875877504, 931609056243993494400]$ |
$0$ |
$0$ |
$32$ |
$12$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$, $C_2$ |
1.5.ae $\times$ 1.5.ad $\times$ 1.5.ac |
| 3.5.aj_bq_aen |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-3$ |
$[-3, 29, 180, 773, 3297, 15404, 76605, 387173, 1950372, 9774629]$ |
$27$ |
$[27, 19683, 2985984, 307546875, 32248529487, 3761479876608, 467631900367659, 59079764836546875, 7440091291058982912, 932181717755442707883]$ |
$0$ |
$0$ |
$10$ |
$6$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
1.5.ad 3 |
| 3.5.ai_bd_acu |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 4 x + 8 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 20, 94, 548, 3158, 15860, 77894, 389948, 1955038, 9766100]$ |
$20$ |
$[20, 11600, 1523780, 215296000, 30832218100, 3871894504400, 475417322416420, 59501228064768000, 7457879671114652180, 931367955870918290000]$ |
$0$ |
$0$ |
$24$ |
$24$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(i, \sqrt{6})\) |
$C_2$, $C_2^2$ |
1.5.ae $\times$ 2.5.ae_i |
| 3.5.ai_be_acy |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 4 x + 9 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 22, 106, 578, 3238, 16192, 78846, 391618, 1958578, 9777702]$ |
$22$ |
$[22, 12980, 1696288, 226371200, 31650524422, 3955200803840, 481251420324158, 59755963554777600, 7471407897745239712, 932474898825522446900]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-26 +2 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.5.ae $\times$ 2.5.ae_j |
| 3.5.ai_bf_adc |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$-2$ |
$[-2, 24, 118, 604, 3278, 16344, 79238, 391484, 1955998, 9772824]$ |
$24$ |
$[24, 14400, 1875384, 235929600, 32050265304, 3993442689600, 483666903669624, 59735426885222400, 7461551890320424344, 932009375688177960000]$ |
$0$ |
$0$ |
$16$ |
$12$ |
$2$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-5}) \) |
$C_2$, $C_2$ |
1.5.ae 2 $\times$ 1.5.a |
| 3.5.ai_bg_adh |
$3$ |
$\F_{5}$ |
$5$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
|
$1 - 8 x + 32 x^{2} - 85 x^{3} + 160 x^{4} - 200 x^{5} + 125 x^{6}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-2$ |
$[-2, 26, 127, 594, 3118, 15821, 78062, 388514, 1949608, 9770826]$ |
$25$ |
$[25, 15275, 1980025, 231339875, 30447855125, 3862876313075, 476458348531225, 59283223224723875, 7437174098712049600, 931818740873960853875]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.4426955.1 |
$A_4\times C_2$ |
simple |
| 3.5.ai_bg_adg |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 4 x + 11 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-2$ |
$[-2, 26, 130, 626, 3278, 16328, 79238, 390626, 1951690, 9765626]$ |
$26$ |
$[26, 15860, 2061800, 244117120, 32038741306, 3989418056000, 483672786014626, 59604644711139840, 7445110105566528200, 931322574601698293300]$ |
$0$ |
$0$ |
$44$ |
$24$ |
$6$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{12})\) |
$C_2$, $C_2^2$ |
1.5.ae $\times$ 2.5.ae_l |
| 3.5.ai_bh_adl |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 28, 139, 612, 3083, 15721, 78314, 389828, 1951663, 9774463]$ |
$27$ |
$[27, 16767, 2173392, 238510575, 30114184752, 3838479772608, 477983065577247, 59483064602199375, 7445000190043130832, 932165795819566927872]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-9 +2 \sqrt{13}})\) |
$C_2$, $D_{4}$ |
1.5.ad $\times$ 2.5.af_n |
| 3.5.ai_bh_adk |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 4 x + 12 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 28, 142, 644, 3238, 16156, 79014, 390076, 1949182, 9763068]$ |
$28$ |
$[28, 17360, 2256268, 251095040, 31627095388, 3946257857360, 482286012066572, 59520757467709440, 7435545892947496156, 931078824995464014800]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-14 +4 \sqrt{2}})\) |
$C_2$, $D_{4}$ |
1.5.ae $\times$ 2.5.ae_m |
| 3.5.ai_bi_adq |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 5 x^{2} )( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 30, 148, 594, 2858, 15108, 78146, 392546, 1955524, 9759870]$ |
$28$ |
$[28, 17696, 2291632, 232525440, 28001290268, 3690297508352, 476971248239276, 59898264082352640, 7459739472894240112, 930773936473397819936]$ |
$0$ |
$0$ |
$24$ |
$24$ |
$6$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{2}, \sqrt{-3})\) |
$C_2$, $C_2^2$ |
1.5.ac $\times$ 2.5.ag_r |
| 3.5.ai_bi_adp |
$3$ |
$\F_{5}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 8 x + 34 x^{2} - 93 x^{3} + 170 x^{4} - 200 x^{5} + 125 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 30, 151, 626, 3008, 15477, 78496, 392178, 1956040, 9772310]$ |
$29$ |
$[29, 18299, 2375477, 244639331, 29396710169, 3778792413227, 479093711198173, 59842076388306563, 7461702113779025216, 931959983641771080779]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.1178891.1 |
$A_4\times C_2$ |
simple |
| 3.5.ai_bi_ado |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 - x + 5 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 30, 154, 658, 3158, 15840, 78734, 390818, 1951138, 9765150]$ |
$30$ |
$[30, 18900, 2459520, 257040000, 30830697150, 3867546009600, 480546460762230, 59633914374720000, 7443003308322395520, 931277345617414372500]$ |
$0$ |
$0$ |
$16$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$, $C_2$ |
1.5.ae $\times$ 1.5.ad $\times$ 1.5.ab |
| 3.5.ai_bj_ads |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-2$ |
$[-2, 32, 166, 668, 3038, 15392, 78566, 393788, 1959358, 9765152]$ |
$32$ |
$[32, 20480, 2672288, 262144000, 29669527072, 3757450711040, 479536310481568, 60088890949632000, 7474389949533895712, 931277654351951974400]$ |
$0$ |
$0$ |
$44$ |
$12$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.5.ae $\times$ 1.5.ac 2 |
| 3.5.ai_bj_adr |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$1$ |
$2$ |
$-2$ |
$[-2, 32, 169, 700, 3183, 15677, 78244, 390100, 1949083, 9756127]$ |
$33$ |
$[33, 21087, 2757744, 274658175, 31064093808, 3827494959552, 477557010073869, 59524407753576975, 7435178620120052208, 930416980553067946752]$ |
$0$ |
$0$ |
$14$ |
$60$ |
$10$ |
\(\Q(\sqrt{-11}) \), \(\Q(\zeta_{5})\) |
$C_2$, $C_4$ |
1.5.ad $\times$ 2.5.af_p |
| 3.5.ai_bk_adu |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 34, 184, 738, 3158, 15244, 77054, 389378, 1953688, 9771154]$ |
$36$ |
$[36, 23328, 3068928, 291600000, 30840252516, 3722781523968, 470336994780948, 59414242996800000, 7452728951964558336, 931850112150151384608]$ |
$0$ |
$0$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.5.ad 2 $\times$ 1.5.ac |
| 3.5.ah_v_abu |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 4 x^{2} - 15 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 19, 86, 591, 3259, 15712, 78175, 392831, 1956398, 9763099]$ |
$24$ |
$[24, 11520, 1423008, 231505920, 31840470264, 3835974205440, 477134309847576, 59942094349271040, 7463080539821056032, 931081655114637753600]$ |
$0$ |
$0$ |
$24$ |
$12$ |
$3$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{-11})\) |
$C_2$, $C_2^2$ |
1.5.ae $\times$ 2.5.ad_e |
| 3.5.ah_w_aby |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} - 15 x^{3} + 25 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-1$ |
$[-1, 21, 95, 609, 3334, 15981, 78595, 393569, 1959179, 9766176]$ |
$26$ |
$[26, 12740, 1543178, 238492800, 32618799616, 3902527412420, 479695772537098, 60055273589875200, 7473705338621861066, 931374997356485427200]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-42 -6 \sqrt{29}})\) |
$C_2$, $D_{4}$ |
1.5.ae $\times$ 2.5.ad_f |
| 3.5.ah_x_acd |
$3$ |
$\F_{5}$ |
$5$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
|
$1 - 7 x + 23 x^{2} - 55 x^{3} + 115 x^{4} - 175 x^{5} + 125 x^{6}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-1$ |
$[-1, 23, 101, 595, 3249, 15695, 77300, 389587, 1952201, 9755083]$ |
$27$ |
$[27, 13527, 1602423, 232028631, 31725751167, 3831830854479, 471824351721792, 59446615346797383, 7447050103389719499, 930317707745221404807]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.12305095.1 |
$S_4\times C_2$ |
simple |
| 3.5.ah_x_acc |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 + x + 5 x^{2} )( 1 - 4 x + 5 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 23, 104, 623, 3379, 16148, 78679, 393023, 1958504, 9762623]$ |
$28$ |
$[28, 14000, 1667008, 243712000, 33085798508, 3944140928000, 480206214537308, 59971529834496000, 7471125593725705408, 931036437877526750000]$ |
$0$ |
$0$ |
$32$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.5.ae 2 $\times$ 1.5.b |
| 3.5.ah_y_ach |
$3$ |
$\F_{5}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 7 x + 24 x^{2} - 59 x^{3} + 120 x^{4} - 175 x^{5} + 125 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 25, 110, 605, 3269, 15832, 77517, 389701, 1954586, 9765045]$ |
$29$ |
$[29, 14819, 1730372, 235814747, 31945643129, 3865810242224, 473141662652821, 59463876907244187, 7456146350377582004, 931267264837529756339]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.29215664.1 |
$S_4\times C_2$ |
simple |
| 3.5.ah_y_acg |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 7 x^{2} - 15 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 25, 113, 633, 3394, 16225, 78553, 391793, 1956479, 9760000]$ |
$30$ |
$[30, 15300, 1795230, 247248000, 33240602400, 3963490841700, 479439438068670, 59783198624064000, 7463383322582171070, 930786355808853120000]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-50 -6 \sqrt{21}})\) |
$C_2$, $D_{4}$ |
1.5.ae $\times$ 2.5.ad_h |
| 3.5.ah_z_acm |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 - 4 x + 8 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 27, 116, 583, 3139, 15552, 76831, 387743, 1952684, 9768627]$ |
$30$ |
$[30, 15660, 1798560, 227070000, 30649266150, 3796702606080, 468994397049390, 59166260213760000, 7448897684999193120, 931608949391820780300]$ |
$0$ |
$0$ |
$12$ |
$24$ |
$4$ |
\(\Q(\sqrt{-11}) \), \(\Q(i, \sqrt{6})\) |
$C_2$, $C_2^2$ |
1.5.ad $\times$ 2.5.ae_i |
| 3.5.ah_z_acl |
$3$ |
$\F_{5}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 7 x + 25 x^{2} - 63 x^{3} + 125 x^{4} - 175 x^{5} + 125 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 27, 119, 611, 3259, 15891, 77636, 389475, 1955639, 9773147]$ |
$31$ |
$[31, 16151, 1863379, 238017287, 31856571571, 3880369374623, 473860949307392, 59429177074303943, 7460168205289474927, 932040174864007852511]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.40529831.1 |
$A_4\times C_2$ |
simple |
| 3.5.ah_z_ack |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 8 x^{2} - 15 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 27, 122, 639, 3379, 16224, 78343, 390431, 1954562, 9761907]$ |
$32$ |
$[32, 16640, 1928576, 249200640, 33084652192, 3963300823040, 478162107320608, 59574985532375040, 7456057425249350528, 930968055341913555200]$ |
$0$ |
$0$ |
$16$ |
$12$ |
$6$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-3}, \sqrt{17})\) |
$C_2$, $C_2^2$ |
1.5.ae $\times$ 2.5.ad_i |
| 3.5.ah_ba_acq |
$3$ |
$\F_{5}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 7 x + 26 x^{2} - 68 x^{3} + 130 x^{4} - 175 x^{5} + 125 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 29, 125, 585, 3104, 15605, 77293, 388625, 1955159, 9779244]$ |
$32$ |
$[32, 17024, 1936928, 228053504, 30324608512, 3809557738112, 471784538663456, 59300166091507712, 7458349887882594848, 932622132633578799104]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.2419571.1 |
$S_4\times C_2$ |
simple |
| 3.5.ah_ba_acp |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 - 4 x + 9 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 29, 128, 613, 3219, 15884, 77783, 389413, 1956224, 9780229]$ |
$33$ |
$[33, 17523, 2002176, 238750875, 31462716813, 3878391103488, 474749675836161, 59419561645978875, 7462409618749079808, 932716178770365536283]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-26 +2 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.5.ad $\times$ 2.5.ae_j |
| 3.5.ah_ba_aco |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 9 x^{2} - 15 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 29, 131, 641, 3334, 16157, 78175, 389441, 1953563, 9768224]$ |
$34$ |
$[34, 18020, 2067778, 249685120, 32622078464, 3946416346340, 477137581838546, 59423853080240640, 7452248129676720802, 931570504625496473600]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-58 -6 \sqrt{13}})\) |
$C_2$, $D_{4}$ |
1.5.ae $\times$ 2.5.ad_j |
| 3.5.ah_bb_acv |
$3$ |
$\F_{5}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 7 x + 27 x^{2} - 73 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 31, 131, 555, 2929, 15379, 77608, 389123, 1952105, 9768991]$ |
$33$ |
$[33, 17919, 2016333, 217482903, 28658222373, 3754305180351, 473689314069312, 59375689591896711, 7446683321665991073, 931643554087041402519]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.3194271.1 |
$S_4\times C_2$ |
simple |
| 3.5.ah_bb_acu |
$3$ |
$\F_{5}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 7 x + 27 x^{2} - 72 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 31, 134, 583, 3039, 15604, 77895, 389919, 1956050, 9781671]$ |
$34$ |
$[34, 18428, 2081752, 227696368, 29704311514, 3809173155584, 475438285000706, 59497009954413568, 7461745622541171448, 932853866069718042428]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.31554496.1 |
$S_4\times C_2$ |
simple |
| 3.5.ah_bb_act |
$3$ |
$\F_{5}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 7 x + 27 x^{2} - 71 x^{3} + 135 x^{4} - 175 x^{5} + 125 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 31, 137, 611, 3149, 15823, 78084, 389971, 1956557, 9783651]$ |
$35$ |
$[35, 18935, 2147495, 238145495, 30771328175, 3862967693375, 476579628320320, 59504599663620615, 7463682671683774235, 933042916592115847175]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.39563351.1 |
$S_4\times C_2$ |
simple |
| 3.5.ah_bb_acs |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )( 1 + 5 x^{2} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$2$ |
$1$ |
$-1$ |
$[-1, 31, 140, 639, 3259, 16036, 78175, 389279, 1953644, 9775351]$ |
$36$ |
$[36, 19440, 2213568, 248832000, 31860085716, 3915890334720, 477132525811908, 59399140589568000, 7452565481524072896, 932250535177878457200]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$2$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-5}) \) |
$C_2$, $C_2$, $C_2$ |
1.5.ae $\times$ 1.5.ad $\times$ 1.5.a |
| 3.5.ah_bc_acz |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 5 x^{2} )( 1 - 6 x + 17 x^{2} - 30 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 33, 140, 549, 2839, 15396, 78763, 391781, 1950620, 9756393]$ |
$35$ |
$[35, 19355, 2167760, 216175995, 27826512175, 3759346734080, 480740926726795, 59781275285316795, 7441032178902924560, 930442523201272818275]$ |
$0$ |
$0$ |
$12$ |
$24$ |
$6$ |
\(\Q(\sqrt{-19}) \), \(\Q(\sqrt{2}, \sqrt{-3})\) |
$C_2$, $C_2^2$ |
1.5.ab $\times$ 2.5.ag_r |
| 3.5.ah_bc_acy |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 5 x^{2} )( 1 - 5 x + 13 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 33, 143, 577, 2944, 15561, 78763, 392033, 1954979, 9770988]$ |
$36$ |
$[36, 19872, 2233764, 226143360, 28799113536, 3798989239968, 480748038025284, 59819826030912000, 7457646189152950596, 931834195878196150272]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-9 +2 \sqrt{13}})\) |
$C_2$, $D_{4}$ |
1.5.ac $\times$ 2.5.af_n |
| 3.5.ah_bc_acx |
$3$ |
$\F_{5}$ |
$5$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
|
$1 - 7 x + 28 x^{2} - 75 x^{3} + 140 x^{4} - 175 x^{5} + 125 x^{6}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-1$ |
$[-1, 33, 146, 605, 3049, 15720, 78665, 391557, 1956206, 9777533]$ |
$37$ |
$[37, 20387, 2300068, 236346491, 29793108217, 3837497853104, 480136763602757, 59746888106691803, 7462330081330354804, 932458842786590399507]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.16537520.2 |
$S_4\times C_2$ |
simple |
| 3.5.ah_bc_acw |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 3 x + 11 x^{2} - 15 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 33, 149, 633, 3154, 15873, 78469, 390353, 1954319, 9776448]$ |
$38$ |
$[38, 20900, 2366678, 246787200, 30809336608, 3875080223300, 478926689820358, 59563035421401600, 7455135827521848278, 932355225364956800000]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-66 -6 \sqrt{5}})\) |
$C_2$, $D_{4}$ |
1.5.ae $\times$ 2.5.ad_l |
| 3.5.ah_bc_acv |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 - 4 x + 11 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 33, 152, 661, 3259, 16020, 78175, 388421, 1949336, 9768153]$ |
$39$ |
$[39, 21411, 2433600, 257467275, 31848630099, 3911943859200, 477138328685967, 59269094666235675, 7436143498629268800, 931563556380096885531]$ |
$0$ |
$0$ |
$32$ |
$24$ |
$3$ |
\(\Q(\sqrt{-11}) \), \(\Q(\zeta_{12})\) |
$C_2$, $C_2^2$ |
1.5.ad $\times$ 2.5.ae_l |
| 3.5.ah_bd_ada |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 5 x^{2} )( 1 - 2 x + 5 x^{2} )( 1 - x + 5 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 35, 158, 623, 3019, 15680, 79183, 393023, 1954454, 9761675]$ |
$40$ |
$[40, 22400, 2527840, 243712000, 29484336200, 3827756441600, 483326261595560, 59971529834496000, 7455645915549902560, 930946061725008560000]$ |
$0$ |
$0$ |
$32$ |
$12$ |
$4$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$, $C_2$ |
1.5.ae $\times$ 1.5.ac $\times$ 1.5.ab |
| 3.5.ah_bd_acz |
$3$ |
$\F_{5}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 7 x + 29 x^{2} - 77 x^{3} + 145 x^{4} - 175 x^{5} + 125 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 35, 161, 651, 3119, 15767, 78616, 390803, 1952027, 9765735]$ |
$41$ |
$[41, 22919, 2595341, 254148791, 30449662741, 3848960777207, 479830846056512, 59632077805823783, 7446386764481290409, 931333001509019055479]$ |
$0$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.3627911.1 |
$A_4\times C_2$ |
simple |
| 3.5.ah_bd_acy |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 5 x^{2} )( 1 - 4 x + 12 x^{2} - 20 x^{3} + 25 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 35, 164, 679, 3219, 15848, 77951, 387871, 1946828, 9765595]$ |
$42$ |
$[42, 23436, 2663136, 264826800, 31439426802, 3869621828352, 475770290162874, 59185679674060800, 7426590804783499104, 931319743703112261036]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-14 +4 \sqrt{2}})\) |
$C_2$, $D_{4}$ |
1.5.ad $\times$ 2.5.ae_m |
| 3.5.ah_be_adc |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
|
|
|
✓ |
|
$( 1 - 2 x + 5 x^{2} )( 1 - 5 x + 15 x^{2} - 25 x^{3} + 25 x^{4} )$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$1$ |
$2$ |
$-1$ |
$[-1, 37, 173, 665, 3044, 15517, 78693, 392305, 1952399, 9752652]$ |
$44$ |
$[44, 24992, 2834348, 260416640, 29707540544, 3788117439392, 480319517933068, 59861403245191680, 7447807936414380524, 930086002718882865152]$ |
$0$ |
$0$ |
$28$ |
$60$ |
$10$ |
\(\Q(\sqrt{-1}) \), \(\Q(\zeta_{5})\) |
$C_2$, $C_4$ |
1.5.ac $\times$ 2.5.af_p |
| 3.5.ah_be_adb |
$3$ |
$\F_{5}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 5 x^{2} )( 1 - 3 x + 5 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 37, 176, 693, 3139, 15532, 77671, 388613, 1948784, 9767677]$ |
$45$ |
$[45, 25515, 2903040, 271096875, 30647754225, 3792438558720, 474054240333285, 59298199553446875, 7434039238731463680, 931518315692713131075]$ |
$0$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.5.ad 2 $\times$ 1.5.ab |
