| 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 |
| 3.7.ap_ds_amx |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-7$ |
$[-7, 17, 284, 2333, 16883, 118508, 827309, 5777621, 40391348, 282574217]$ |
$27$ |
$[27, 59319, 34012224, 13464285939, 4769628681537, 1640360041721856, 561105308109354399, 192007660012577296875, 65773842741647278356672, 22547238253611059320055919]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
1.7.af 3 |
| 3.7.ao_di_alk |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 7 x^{2} )( 1 - 5 x + 7 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-6$ |
$[-6, 26, 324, 2450, 17094, 118508, 825546, 5769314, 40366188, 282519146]$ |
$36$ |
$[36, 73008, 38211264, 14126463936, 4829415508116, 1640360041721856, 559905950862077436, 191731184558241120000, 65732846304644610541632, 22542842987256138553841328]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.7.af 2 $\times$ 1.7.ae |
| 3.7.an_cy_ajx |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 7 x^{2} )( 1 - 5 x + 7 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-5$ |
$[-5, 33, 340, 2429, 16825, 117612, 824455, 5772821, 40388380, 282573753]$ |
$45$ |
$[45, 83655, 39890880, 14007611475, 4753194387975, 1627897667235840, 559163750773149945, 191847905326070296875, 65769006595978601167680, 22547201221351091583215775]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.7.af 2 $\times$ 1.7.ad |
| 3.7.an_cz_akc |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 7 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-5$ |
$[-5, 35, 364, 2567, 17305, 118508, 823783, 5761007, 40341028, 282464075]$ |
$48$ |
$[48, 89856, 42928704, 14821208064, 4889951756688, 1640360041721856, 558709157229483504, 191455107206130892800, 65691875420472321139392, 22538448577696454233249536]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.7.af $\times$ 1.7.ae 2 |
| 3.7.am_co_aik |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 7 x^{2} )( 1 - 5 x + 7 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-4$ |
$[-4, 38, 338, 2354, 16616, 117752, 826808, 5778146, 40383086, 282516278]$ |
$54$ |
$[54, 91260, 39680928, 13583138400, 4693974261174, 1629844913249280, 560764481120763498, 192025133181414000000, 65760380398145050952544, 22542614089580303490786300]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \) |
$C_2$, $C_2$ |
1.7.af 2 $\times$ 1.7.ac |
| 3.7.am_cp_aip |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 7 x + 25 x^{2} - 49 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-4$ |
$[-4, 40, 359, 2452, 16861, 117973, 826220, 5775892, 40378823, 282494075]$ |
$57$ |
$[57, 97071, 42224004, 14146059759, 4762715284272, 1632875028862896, 560363983937994531, 191950117471752464175, 65753434806167474684532, 22540842492703355938081536]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.3725.1 |
$C_2$, $D_{4}$ |
1.7.af $\times$ 2.7.ah_z |
| 3.7.am_cq_aiu |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 7 x^{2} )( 1 - 3 x + 7 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-4$ |
$[-4, 42, 380, 2546, 17036, 117612, 822692, 5764514, 40363220, 282518682]$ |
$60$ |
$[60, 102960, 44815680, 14696510400, 4812775212300, 1627897667235840, 557968543586170980, 191571659905523040000, 65728013173316178310080, 22542805962215088027706800]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$, $C_2$ |
1.7.af $\times$ 1.7.ae $\times$ 1.7.ad |
| 3.7.am_cr_aiy |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 7 x^{2} )^{3}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-4$ |
$[-4, 44, 404, 2684, 17516, 118508, 822020, 5752700, 40315868, 282409004]$ |
$64$ |
$[64, 110592, 48228544, 15550119936, 4951246821184, 1640360041721856, 557514921731870656, 191179427383011704832, 65650930073203486053952, 22534055024764986201157632]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
1.7.ae 3 |
| 3.7.al_cd_ags |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 6 x + 18 x^{2} - 42 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-3$ |
$[-3, 39, 306, 2215, 16467, 117936, 825381, 5765231, 40350582, 282508239]$ |
$60$ |
$[60, 90480, 36164880, 12804729600, 4652481286500, 1632390679745280, 559793180264991180, 191595514633735680000, 65707433404317129112560, 22541972792430127694502000]$ |
$None$ |
$0$ |
$24$ |
$24$ |
$4$ |
\(\Q(\sqrt{-3}) \), \(\Q(i, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.7.af $\times$ 2.7.ag_s |
| 3.7.al_ce_agx |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - x + 7 x^{2} )( 1 - 5 x + 7 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-3$ |
$[-3, 41, 324, 2285, 16647, 118508, 827817, 5773109, 40366188, 282530321]$ |
$63$ |
$[63, 95823, 38211264, 13192623171, 4702758107733, 1640360041721856, 561450897151678107, 191857490607260716875, 65732846304644610541632, 22543734874120663250368503]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.7.af 2 $\times$ 1.7.ab |
| 3.7.al_cf_ahc |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 6 x + 20 x^{2} - 42 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-3$ |
$[-3, 43, 342, 2351, 16767, 118660, 828405, 5774831, 40362246, 282485443]$ |
$66$ |
$[66, 101244, 40294584, 13562241264, 4736077364766, 1642465590397632, 561851157353198394, 191914806012143385600, 65726428749628338206856, 22540153622868915953014524]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.21312.1 |
$C_2$, $D_{4}$ |
1.7.af $\times$ 2.7.ag_u |
| 3.7.al_cg_ahh |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 6 x + 21 x^{2} - 42 x^{3} + 49 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-3$ |
$[-3, 45, 360, 2413, 16827, 118404, 827397, 5772917, 40354632, 282444405]$ |
$69$ |
$[69, 106743, 42416784, 13914697251, 4752671352999, 1638894270843648, 561165128410352073, 191851115047590091275, 65714030199587768598576, 22536879029879021279109183]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.13888.1 |
$C_2$, $D_{4}$ |
1.7.af $\times$ 2.7.ag_v |
| 3.7.al_ch_ahn |
$3$ |
$\F_{7}$ |
$7$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 11 x + 59 x^{2} - 195 x^{3} + 413 x^{4} - 539 x^{5} + 343 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-3$ |
$[-3, 47, 375, 2427, 16517, 116387, 821048, 5762531, 40352631, 282467967]$ |
$71$ |
$[71, 110831, 43933877, 13983436439, 4666007907401, 1611031149891527, 556855969625947328, 191505738801887923847, 65710774036055835559223, 22538759336355737710643471]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.400967.1 |
$A_4\times C_2$ |
simple |
| 3.7.al_ch_ahm |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 7 x^{2} )( 1 - 2 x + 7 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-3$ |
$[-3, 47, 378, 2471, 16827, 117752, 825045, 5769839, 40357926, 282461207]$ |
$72$ |
$[72, 112320, 44579808, 14251161600, 4752812767032, 1629844913249280, 559565852387925672, 191748632567132160000, 65719392352139385778464, 22538219724640995377745600]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \) |
$C_2$, $C_2$, $C_2$ |
1.7.af $\times$ 1.7.ae $\times$ 1.7.ac |
| 3.7.al_ci_ahr |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 3 x + 7 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-3$ |
$[-3, 49, 396, 2525, 16767, 116716, 821601, 5768021, 40385412, 282573289]$ |
$75$ |
$[75, 117975, 46785600, 14572861875, 4736816720625, 1615529973657600, 557228911685436975, 191688283559051296875, 65764170805896642859200, 22547164189151946740199375]$ |
$None$ |
$0$ |
$36$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.7.af $\times$ 1.7.ad 2 |
| 3.7.al_ci_ahq |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 7 x^{2} )( 1 - 7 x + 25 x^{2} - 49 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-3$ |
$[-3, 49, 399, 2569, 17072, 117973, 824457, 5767585, 40353663, 282439004]$ |
$76$ |
$[76, 119472, 47436844, 14841767616, 4822415452096, 1632875028862896, 559166211264067084, 191673724874007098112, 65712451089307136679292, 22536448473111893097541632]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.3725.1 |
$C_2$, $D_{4}$ |
1.7.ae $\times$ 2.7.ah_z |
| 3.7.al_cj_ahu |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 7 x^{2} )( 1 - 4 x + 7 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-3$ |
$[-3, 51, 420, 2663, 17247, 117612, 820929, 5756207, 40338060, 282463611]$ |
$80$ |
$[80, 126720, 50348480, 15419289600, 4873102876400, 1627897667235840, 556775891143160720, 191295812255971737600, 65687045301605313884480, 22538411559872913691641600]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.7.ae 2 $\times$ 1.7.ad |
| 3.7.ak_bt_aff |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 5 x + 13 x^{2} - 35 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 40, 289, 2212, 16733, 118333, 823954, 5764372, 40372453, 282551675]$ |
$69$ |
$[69, 92391, 34480404, 12787745919, 4727062720944, 1637900701675056, 558825243763515063, 191566927803691316175, 65743058244179560877892, 22545439165532314764884736]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.24389.1 |
$C_2$, $C_4$ |
1.7.af $\times$ 2.7.af_n |
| 3.7.ak_bu_afk |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 + 7 x^{2} )( 1 - 5 x + 7 x^{2} )^{2}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$-2$ |
$[-2, 42, 304, 2258, 16858, 118908, 826054, 5768546, 40378768, 282574842]$ |
$72$ |
$[72, 97344, 36111744, 13039812864, 4762544934312, 1645923601760256, 560251539904401144, 191705623808400000000, 65753344523145944449152, 22547288135426748620756544]$ |
$None$ |
$0$ |
$24$ |
$12$ |
$2$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.7.af 2 $\times$ 1.7.a |
| 3.7.ak_bv_afp |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 5 x + 15 x^{2} - 35 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 44, 319, 2300, 16933, 119201, 827104, 5768996, 40370593, 282550139]$ |
$75$ |
$[75, 102375, 37770300, 13270359375, 4783635606000, 1650012929838000, 560965499956055325, 191720589960793359375, 65740026518341194570300, 22545316578869898559200000]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.62181.1 |
$C_2$, $D_{4}$ |
1.7.af $\times$ 2.7.af_p |
| 3.7.ak_bw_afv |
$3$ |
$\F_{7}$ |
$7$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 10 x + 48 x^{2} - 151 x^{3} + 336 x^{4} - 490 x^{5} + 343 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 46, 331, 2298, 16698, 118081, 823268, 5754690, 40321276, 282432586]$ |
$77$ |
$[77, 106183, 38913413, 13242825211, 4716236247107, 1634371245422839, 558358990899492629, 191245468376951707411, 65659731385027467668288, 22535936195083358308721383]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.2476099.1 |
$C_6$ |
simple |
| 3.7.ak_bw_afu |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 5 x + 16 x^{2} - 35 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 46, 334, 2338, 16958, 119224, 827314, 5767426, 40356658, 282511886]$ |
$78$ |
$[78, 107484, 39458016, 13480213344, 4790434219038, 1650333728848896, 561108653042933346, 191668447132197360000, 65717329386644766893088, 22542263711395652400454044]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.57800.1 |
$C_2$, $D_{4}$ |
1.7.af $\times$ 2.7.af_q |
| 3.7.ak_bx_aga |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 7 x^{2} )( 1 - 6 x + 18 x^{2} - 42 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 48, 346, 2332, 16678, 117936, 823618, 5756924, 40325422, 282453168]$ |
$80$ |
$[80, 111360, 40629680, 13434470400, 4710799682000, 1632390679745280, 558596627678473520, 191319632635310899200, 65666478359851384193360, 22537578552502661651424000]$ |
$None$ |
$0$ |
$24$ |
$24$ |
$4$ |
\(\Q(\sqrt{-3}) \), \(\Q(i, \sqrt{5})\) |
$C_2$, $C_2^2$ |
1.7.ae $\times$ 2.7.ag_s |
| 3.7.ak_bx_afz |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 5 x + 17 x^{2} - 35 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 48, 349, 2372, 16933, 118989, 826894, 5765492, 40344613, 282483003]$ |
$81$ |
$[81, 112671, 41176836, 13670259759, 4783070555856, 1647056804558256, 560822888561694147, 191604190204656248175, 65697713371940048165268, 22539958845783200991726336]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.4901.1 |
$C_2$, $D_{4}$ |
1.7.af $\times$ 2.7.af_r |
| 3.7.ak_by_agf |
$3$ |
$\F_{7}$ |
$7$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
|
$1 - 10 x + 50 x^{2} - 161 x^{3} + 350 x^{4} - 490 x^{5} + 343 x^{6}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-2$ |
$[-2, 50, 361, 2362, 16608, 117545, 823534, 5760082, 40334572, 282471750]$ |
$83$ |
$[83, 116615, 42378887, 13607221275, 4691372514113, 1626994337621375, 558538943781688211, 191424468768098663475, 65681371637510592633536, 22539061206955685288098575]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.24504179.1 |
$S_4\times C_2$ |
simple |
| 3.7.ak_by_age |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 7 x^{2} )( 1 - x + 7 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-2$ |
$[-2, 50, 364, 2402, 16858, 118508, 826054, 5764802, 40341028, 282475250]$ |
$84$ |
$[84, 117936, 42928704, 13841440704, 4761706718244, 1640360041721856, 560250801211117548, 191581231384686124800, 65691875420472321139392, 22539340290700203434873136]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$, $C_2$ |
1.7.af $\times$ 1.7.ae $\times$ 1.7.ab |
| 3.7.ak_bz_agk |
$3$ |
$\F_{7}$ |
$7$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 10 x + 51 x^{2} - 166 x^{3} + 357 x^{4} - 490 x^{5} + 343 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 52, 376, 2388, 16488, 116920, 823226, 5765724, 40354270, 282490672]$ |
$86$ |
$[86, 121948, 44162978, 13762075696, 4658150804726, 1618368845763772, 558329821626191666, 191611914119074964224, 65713443926415447470702, 22540570795576448403639388]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.12178624.1 |
$S_4\times C_2$ |
simple |
| 3.7.ak_bz_agj |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 5 x + 19 x^{2} - 35 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 52, 379, 2428, 16733, 117793, 825004, 5766916, 40351393, 282489467]$ |
$87$ |
$[87, 123279, 44715564, 13994755359, 4726539147312, 1630429805165616, 559536102533813289, 191651465905654779375, 65708754933069306113292, 22540474672271024195660544]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.9725.1 |
$C_2$, $D_{4}$ |
1.7.af $\times$ 2.7.af_t |
| 3.7.ak_bz_agi |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 7 x^{2} )( 1 - 6 x + 20 x^{2} - 42 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 52, 382, 2468, 16978, 118660, 826642, 5766524, 40337086, 282430372]$ |
$88$ |
$[88, 124608, 45269224, 14229236736, 4795443628888, 1642465590397632, 560650205860272616, 191638464260035313664, 65685461865479142622936, 22535759737562919570833088]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.21312.1 |
$C_2$, $D_{4}$ |
1.7.ae $\times$ 2.7.ag_u |
| 3.7.ak_ca_ago |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 3 x + 7 x^{2} )( 1 - 2 x + 7 x^{2} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 54, 394, 2450, 16558, 116856, 823954, 5773346, 40380118, 282515814]$ |
$90$ |
$[90, 128700, 46539360, 14131260000, 4677800643450, 1617462425779200, 558824103126708390, 191865363956838000000, 65755545242320535283360, 22542577064915201368717500]$ |
$None$ |
$0$ |
$24$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \), \(\Q(\sqrt{-6}) \) |
$C_2$, $C_2$, $C_2$ |
1.7.af $\times$ 1.7.ad $\times$ 1.7.ac |
| 3.7.ak_ca_agn |
$3$ |
$\F_{7}$ |
$7$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 10 x + 52 x^{2} - 169 x^{3} + 364 x^{4} - 490 x^{5} + 343 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 54, 397, 2490, 16798, 117633, 824864, 5769762, 40360276, 282478194]$ |
$91$ |
$[91, 130039, 47095867, 14364237979, 4744758184621, 1628188753462999, 559440586548193987, 191746078729927173907, 65723224633291763731648, 22539575190750992919962599]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.4770787.1 |
$A_4\times C_2$ |
simple |
| 3.7.ak_ca_agm |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 4 x + 7 x^{2} )( 1 - 6 x + 21 x^{2} - 42 x^{3} + 49 x^{4} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-2$ |
$[-2, 54, 400, 2530, 17038, 118404, 825634, 5764610, 40329472, 282389334]$ |
$92$ |
$[92, 131376, 47653424, 14599026624, 4812245621132, 1638894270843648, 559965643297751972, 191574865005304225536, 65673071043379567114256, 22532485782908781704677296]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.13888.1 |
$C_2$, $D_{4}$ |
1.7.ae $\times$ 2.7.ag_v |
| 3.7.ak_cb_agr |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 3 x + 7 x^{2} )( 1 - 7 x + 25 x^{2} - 49 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-2$ |
$[-2, 56, 415, 2548, 16803, 117077, 823366, 5771092, 40375855, 282493611]$ |
$95$ |
$[95, 136895, 49521980, 14716896975, 4746304811600, 1620469520571440, 558424991759101205, 191790410661932100975, 65748600161030690773580, 22540805470947977630841600]$ |
$None$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-19}) \), 4.0.3725.1 |
$C_2$, $D_{4}$ |
1.7.ad $\times$ 2.7.ah_z |
| 3.7.ak_cb_agq |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 2 x + 7 x^{2} )( 1 - 4 x + 7 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 56, 418, 2588, 17038, 117752, 823282, 5761532, 40332766, 282406136]$ |
$96$ |
$[96, 138240, 50083488, 14952038400, 4812388807776, 1629844913249280, 558369785712578208, 191472530091304550400, 65678429853734041509984, 22533826216321205439667200]$ |
$None$ |
$0$ |
$48$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \) |
$C_2$, $C_2$ |
1.7.ae 2 $\times$ 1.7.ac |
| 3.7.ak_cc_agu |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 7 x^{2} )( 1 - 3 x + 7 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-2$ |
$[-2, 58, 436, 2642, 16978, 116716, 819838, 5759714, 40360252, 282518218]$ |
$100$ |
$[100, 145200, 52561600, 15289560000, 4796192252500, 1615529973657600, 556037840198563900, 191412267980899680000, 65723180397352829915200, 22542768937234848538830000]$ |
$None$ |
$0$ |
$36$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-19}) \) |
$C_2$, $C_2$ |
1.7.ae $\times$ 1.7.ad 2 |
| 3.7.aj_bj_ads |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 8 x^{2} - 28 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$2$ |
$1$ |
$-1$ |
$[-1, 39, 272, 2255, 16949, 117936, 822947, 5770991, 40382984, 282508239]$ |
$78$ |
$[78, 91260, 32760936, 13026452400, 4787838907098, 1632410608570560, 558141140442602886, 191787062249502720000, 65760214491382195402488, 22541972682167303266921500]$ |
$None$ |
$0$ |
$24$ |
$24$ |
$4$ |
\(\Q(\sqrt{-3}) \), \(\Q(i, \sqrt{10})\) |
$C_2$, $C_2^2$ |
1.7.af $\times$ 2.7.ae_i |
| 3.7.aj_bk_adx |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 + x + 7 x^{2} )( 1 - 5 x + 7 x^{2} )^{2}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$1$ |
$2$ |
$-1$ |
$[-1, 41, 284, 2285, 17069, 118508, 824291, 5773109, 40391348, 282530321]$ |
$81$ |
$[81, 95823, 34012224, 13192623171, 4822331760891, 1640360041721856, 559052182657124181, 191857490607260716875, 65773842741647278356672, 22543734874120663250368503]$ |
$None$ |
$0$ |
$78$ |
$18$ |
$3$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.7.af 2 $\times$ 1.7.b |
| 3.7.aj_bl_aec |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 10 x^{2} - 28 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 43, 296, 2311, 17149, 118900, 824963, 5772271, 40388840, 282524243]$ |
$84$ |
$[84, 100464, 35281008, 13335189504, 4845286603164, 1645816121494272, 559508091334548132, 191829586750048665600, 65769756136310827499472, 22543249941543342224055024]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.2048.2 |
$C_2$, $C_4$ |
1.7.af $\times$ 2.7.ae_k |
| 3.7.aj_bm_aei |
$3$ |
$\F_{7}$ |
$7$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
|
$1 - 9 x + 38 x^{2} - 112 x^{3} + 266 x^{4} - 441 x^{5} + 343 x^{6}$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$3$ |
$0$ |
$-1$ |
$[-1, 45, 305, 2297, 16974, 118185, 821547, 5757537, 40346945, 282434600]$ |
$86$ |
$[86, 104060, 36096350, 13240594400, 4794339367136, 1635819081825500, 557193261508696262, 191339982259009865600, 65701512455397896151950, 22536096965623129594956800]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.30088184.1 |
$S_4\times C_2$ |
simple |
| 3.7.aj_bm_aeh |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 11 x^{2} - 28 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 45, 308, 2333, 17189, 119124, 825131, 5769557, 40380284, 282510405]$ |
$87$ |
$[87, 105183, 36569232, 13454693811, 4856713533717, 1648938266696448, 559622658311689227, 191739316707149863275, 65755815233310693563184, 22542145617400040024253783]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.138768.1 |
$C_2$, $D_{4}$ |
1.7.af $\times$ 2.7.ae_l |
| 3.7.aj_bn_aen |
$3$ |
$\F_{7}$ |
$7$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 9 x + 39 x^{2} - 117 x^{3} + 273 x^{4} - 441 x^{5} + 343 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 47, 317, 2315, 16979, 118331, 821960, 5756867, 40347857, 282466967]$ |
$89$ |
$[89, 108847, 37405187, 13339526391, 4796042024159, 1637863504126903, 557473962960800576, 191317740292278438471, 65702998610871049393937, 22538679394105663381021087]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.1305639.1 |
$A_4\times C_2$ |
simple |
| 3.7.aj_bn_aem |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 12 x^{2} - 28 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 47, 320, 2351, 17189, 119192, 824963, 5765999, 40369640, 282502007]$ |
$90$ |
$[90, 109980, 37878840, 13551735600, 4856642851950, 1649887421757120, 559509476998517730, 191621020997352960000, 65738473828071997222440, 22541475295756331716779900]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.131328.1 |
$C_2$, $D_{4}$ |
1.7.af $\times$ 2.7.ae_m |
| 3.7.aj_bo_aes |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 4 x + 7 x^{2} )( 1 - 5 x + 13 x^{2} - 35 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 49, 329, 2329, 16944, 118333, 822191, 5756065, 40347293, 282496604]$ |
$92$ |
$[92, 113712, 38737244, 13416651456, 4786315987392, 1637900701675056, 557630760132042332, 191291086967982772992, 65702080994967335097452, 22541044249884261647020032]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.24389.1 |
$C_2$, $C_4$ |
1.7.ae $\times$ 2.7.af_n |
| 3.7.aj_bo_aer |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 13 x^{2} - 28 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 49, 332, 2365, 17149, 119116, 824627, 5762581, 40360004, 282505289]$ |
$93$ |
$[93, 114855, 39211776, 13626971475, 4845127076823, 1648826948321280, 559282060852288041, 191507412525777976875, 65722777207740542585088, 22541737097470480089861375]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.7025.1 |
$C_2$, $D_{4}$ |
1.7.af $\times$ 2.7.ae_n |
| 3.7.aj_bp_aex |
$3$ |
$\F_{7}$ |
$7$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 9 x + 41 x^{2} - 127 x^{3} + 287 x^{4} - 441 x^{5} + 343 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 51, 341, 2339, 16869, 118203, 822408, 5756067, 40347539, 282524291]$ |
$95$ |
$[95, 118655, 40094465, 13472681975, 4765238252225, 1636097906252735, 557777384517009920, 191291127247769841575, 65702482696227733419695, 22543253749683243072523775]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.244361927.1 |
$S_4\times C_2$ |
simple |
| 3.7.aj_bp_aew |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 7 x^{2} )( 1 + 7 x^{2} )$ |
$[0,0,\frac{1}{2},\frac{1}{2},1,1]$ |
$1$ |
$2$ |
$1$ |
$1$ |
$2$ |
$-1$ |
$[-1, 51, 344, 2375, 17069, 118908, 824291, 5760239, 40353608, 282519771]$ |
$96$ |
$[96, 119808, 40569984, 13681115136, 4822242966816, 1645923601760256, 559054007578523616, 191429583261696000000, 65712360862558465840512, 22542892859348070835811328]$ |
$None$ |
$0$ |
$24$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$, $C_2$ |
1.7.af $\times$ 1.7.ae $\times$ 1.7.a |
| 3.7.aj_bp_aev |
$3$ |
$\F_{7}$ |
$7$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 9 x + 41 x^{2} - 125 x^{3} + 287 x^{4} - 441 x^{5} + 343 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 51, 347, 2411, 17269, 119607, 826048, 5763123, 40351091, 282472991]$ |
$97$ |
$[97, 120959, 41046811, 13891052519, 4879565729107, 1655693270684999, 560247160804921792, 191525435461048158791, 65708266761304067998357, 22539159970511717275802039]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.3627911.1 |
$A_4\times C_2$ |
simple |
| 3.7.aj_bq_afd |
$3$ |
$\F_{7}$ |
$7$ |
✓ |
✓ |
✓ |
|
|
|
✓ |
|
$1 - 9 x + 42 x^{2} - 133 x^{3} + 294 x^{4} - 441 x^{5} + 343 x^{6}$ |
$[0,\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2},1]$ |
$2$ |
$1$ |
$2$ |
$3$ |
$0$ |
$-1$ |
$[-1, 53, 350, 2309, 16559, 117320, 821309, 5754389, 40340006, 282512033]$ |
$97$ |
$[97, 122511, 41003452, 13303346979, 4678048479367, 1623844456271856, 557031695003568049, 191235483740749262763, 65690218868207530794148, 22542275480741043427678431]$ |
$None$ |
$0$ |
$6$ |
$6$ |
$1$ |
6.0.1714608.1 |
$D_{6}$ |
simple |
| 3.7.aj_bq_afc |
$3$ |
$\F_{7}$ |
$7$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
|
$1 - 9 x + 42 x^{2} - 132 x^{3} + 294 x^{4} - 441 x^{5} + 343 x^{6}$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 53, 353, 2345, 16754, 117953, 822779, 5757761, 40350017, 282544328]$ |
$98$ |
$[98, 123676, 41478794, 13508387424, 4732912055648, 1632626817855292, 558027883801579394, 191347369566177976704, 65706517812209444621738, 22544852863465723504086016]$ |
$None$ |
$0$ |
$2$ |
$2$ |
$1$ |
6.0.256065624.1 |
$S_4\times C_2$ |
simple |
| 3.7.aj_bq_afb |
$3$ |
$\F_{7}$ |
$7$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 5 x + 7 x^{2} )( 1 - 4 x + 15 x^{2} - 28 x^{3} + 49 x^{4} )$ |
$[0,0,0,1,1,1]$ |
$0$ |
$3$ |
$0$ |
$3$ |
$0$ |
$-1$ |
$[-1, 53, 356, 2381, 16949, 118580, 824123, 5759861, 40351820, 282538493]$ |
$99$ |
$[99, 124839, 41955408, 13714937379, 4788093539889, 1641348592595712, 558939213215845407, 191417022372347246475, 65709450332466262269552, 22544387121482673630410799]$ |
$None$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), 4.0.56592.1 |
$C_2$, $D_{4}$ |
1.7.af $\times$ 2.7.ae_p |
