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 |
2.53.abc_lq |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 14 x + 53 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$26$ |
$[26, 2630, 147842, 7885518, 418180906, 22164419990, 1174712737042, 62259709652638, 3299763776528186, 174887471931890150]$ |
$1600$ |
$[1600, 7398400, 22010689600, 62220544000000, 174881370619240000, 491260208896217113600, 1379948138313462349633600, 3876270248074620801024000000, 10888440371335229796126157825600, 30585627564787934537419365842560000]$ |
$1$ |
$1$ |
$16$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.53.ao 2 |
2.53.abb_lc |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 14 x + 53 x^{2} )( 1 - 13 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$27$ |
$[27, 2657, 148230, 7889649, 418216527, 22164671414, 1174714088211, 62259713093761, 3299763740030190, 174887471182673657]$ |
$1640$ |
$[1640, 7471840, 22068253280, 62253129328000, 174896266901112200, 491265781555949271040, 1379949725547817499669960, 3876270462317906554239936000, 10888440250900468050520884806240, 30585627433759356733750471587071200]$ |
$0$ |
$0$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.53.ao $\times$ 1.53.an |
2.53.aba_kn |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 26 x + 273 x^{2} - 1378 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$28$ |
$[28, 2680, 148462, 7890564, 418205088, 22164380110, 1174710295696, 62259676272324, 3299763453842806, 174887469421985400]$ |
$1679$ |
$[1679, 7533673, 22102523900, 62260330364729, 174891482107341079, 491259324938320464400, 1379945270436077533316351, 3876268169826562594759305449, 10888439306549756228148866255900, 30585627125837041442419895105561353]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.21056.1 |
$D_{4}$ |
simple |
2.53.aba_ko |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 14 x + 53 x^{2} )( 1 - 12 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$28$ |
$[28, 2682, 148540, 7892174, 418228748, 22164655914, 1174712973644, 62259698390686, 3299763609603580, 174887470340952282]$ |
$1680$ |
$[1680, 7539840, 22114244880, 62273046528000, 174901377579104400, 491265438007895591040, 1379948416252656408414480, 3876269546908867506241536000, 10888439820523476923748385898640, 30585627286552834048192531370371200]$ |
$8$ |
$8$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-17}) \) |
$C_2$, $C_2$ |
1.53.ao $\times$ 1.53.am |
2.53.aba_kp |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 13 x + 53 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$28$ |
$[28, 2684, 148618, 7893780, 418252148, 22164922838, 1174715439380, 62259716534884, 3299763703532194, 174887470433457164]$ |
$1681$ |
$[1681, 7546009, 22125967504, 62285731721161, 174911164451840041, 491271354278895456256, 1379951312783998307372881, 3876270676561204148783373129, 10888440130465707637019323802896, 30585627302730779491406930714801449]$ |
$2$ |
$2$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
1.53.an 2 |
2.53.az_jz |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 25 x + 259 x^{2} - 1325 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$29$ |
$[29, 2703, 148703, 7891931, 418205494, 22164304527, 1174709546263, 62259674411923, 3299763501463109, 174887470298403078]$ |
$1719$ |
$[1719, 7596261, 22138294491, 62271116769861, 174891652336898064, 491257649722771833381, 1379944390069758244971411, 3876268053998537636957979525, 10888439463685493316672942777039, 30585627279111511943817719054628096]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.122525.3 |
$D_{4}$ |
simple |
2.53.az_ka |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 14 x + 53 x^{2} )( 1 - 11 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$29$ |
$[29, 2705, 148778, 7893393, 418225369, 22164513590, 1174711321813, 62259686728513, 3299763570508034, 174887470603558025]$ |
$1720$ |
$[1720, 7602400, 22149554560, 62282662000000, 174899964521176600, 491262283483173529600, 1379946475827060423130840, 3876268820825474804952000000, 10888439691517414020339901521280, 30585627332479288350588378523660000]$ |
$6$ |
$6$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-91}) \) |
$C_2$, $C_2$ |
1.53.ao $\times$ 1.53.al |
2.53.az_kb |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 25 x + 261 x^{2} - 1325 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$29$ |
$[29, 2707, 148853, 7894851, 418244994, 22164714523, 1174712914313, 62259695852643, 3299763593896409, 174887470356194022]$ |
$1721$ |
$[1721, 7608541, 22160816189, 62294176191941, 174908172262931536, 491266737062273780821, 1379948346555038087766749, 3876269388890961059842746725, 10888439768693520024854053854161, 30585627289218423473550392443703296]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.54725.1 |
$D_{4}$ |
simple |
2.53.az_kc |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 13 x + 53 x^{2} )( 1 - 12 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$29$ |
$[29, 2709, 148928, 7896305, 418264369, 22164907338, 1174714324813, 62259701831809, 3299763573105584, 174887469591735789]$ |
$1722$ |
$[1722, 7614684, 22172079384, 62305659351936, 174916275565156482, 491271010726944704256, 1379950003487331247738578, 3876269761152114505695419904, 10888439700088721270556714968856, 30585627155524257436480527158739324]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-17}) \) |
$C_2$, $C_2$ |
1.53.an $\times$ 1.53.am |
2.53.ay_jk |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 24 x + 244 x^{2} - 1272 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$30$ |
$[30, 2722, 148806, 7890934, 418179390, 22164019954, 1174707658182, 62259668344606, 3299763522984318, 174887470627870882]$ |
$1758$ |
$[1758, 7647300, 22153473918, 62263245978000, 174880736006125998, 491251342379661087300, 1379942172122324577750894, 3876267676249360689302016000, 10888439534700397622230298636862, 30585627336731302686760241197306500]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.223488.3 |
$D_{4}$ |
simple |
2.53.ay_jl |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 24 x + 245 x^{2} - 1272 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$30$ |
$[30, 2724, 148878, 7892260, 418196190, 22164183798, 1174708974966, 62259677791684, 3299763591802134, 174887471201742564]$ |
$1759$ |
$[1759, 7653409, 22164272464, 62273714959161, 174887761847933839, 491254973858428631296, 1379943718960625979747799, 3876268264421368470904303209, 10888439761782919017336448749136, 30585627437094269789626558870597249]$ |
$10$ |
$10$ |
$4$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{5})\) |
$C_2^2$ |
simple |
2.53.ay_jm |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 14 x + 53 x^{2} )( 1 - 10 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$30$ |
$[30, 2726, 148950, 7893582, 418212750, 22164340214, 1174710133830, 62259684654238, 3299763626031870, 174887471382390086]$ |
$1760$ |
$[1760, 7659520, 22175072480, 62284152832000, 174894687404280800, 491258440709795799040, 1379945080289247659364320, 3876268691681735521075200000, 10888439874732951658682042275040, 30585627468687257948409683125657600]$ |
$14$ |
$14$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.53.ao $\times$ 1.53.ak |
2.53.ay_jn |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 24 x + 247 x^{2} - 1272 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$30$ |
$[30, 2728, 149022, 7894900, 418229070, 22164489214, 1174711135782, 62259688975780, 3299763626957862, 174887471198892088]$ |
$1761$ |
$[1761, 7665633, 22185873972, 62294559602409, 174901512677783001, 491261743200448472976, 1379946257292433423597953, 3876268960739524210419227913, 10888439877788502649132822238676, 30585627436595757096240455556848913]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.359568.1 |
$D_{4}$ |
simple |
2.53.ay_jo |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 24 x + 248 x^{2} - 1272 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$30$ |
$[30, 2730, 149094, 7896214, 418245150, 22164630810, 1174711981830, 62259690799774, 3299763595859262, 174887470680040650]$ |
$1762$ |
$[1762, 7671748, 22196676946, 62304935276304, 174908237671086082, 491264881597089520900, 1379947251154433239564018, 3876269074300810035133415424, 10888439775170473428928149865954, 30585627345855141460840008021292228]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.205056.2 |
$D_{4}$ |
simple |
2.53.ay_jp |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 13 x + 53 x^{2} )( 1 - 11 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$30$ |
$[30, 2732, 149166, 7897524, 418260990, 22164765014, 1174712672982, 62259690169636, 3299763534010038, 174887469854341532]$ |
$1763$ |
$[1763, 7677865, 22207481408, 62315279859625, 174914862386865323, 491267856166438973440, 1379948063059503359614499, 3876269035068681673434143625, 10888439571082659794057312117312, 30585627201450711542127820499908825]$ |
$6$ |
$6$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-91}) \) |
$C_2$, $C_2$ |
1.53.an $\times$ 1.53.al |
2.53.ay_jq |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 12 x + 53 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$30$ |
$[30, 2734, 149238, 7898830, 418276590, 22164891838, 1174713210246, 62259687128734, 3299763442678974, 174887468750014414]$ |
$1764$ |
$[1764, 7683984, 22218287364, 62325593358336, 174921386827825764, 491270667175234202256, 1379948694191906447701764, 3876268845743241043021922304, 10888439269711751915194702226916, 30585627008317736090048996734567824]$ |
$16$ |
$16$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-17}) \) |
$C_2$ |
1.53.am 2 |
2.53.ax_iv |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 23 x + 229 x^{2} - 1219 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$31$ |
$[31, 2739, 148855, 7889411, 418154186, 22163827707, 1174707089699, 62259672066019, 3299763563132611, 174887470468463334]$ |
$1797$ |
$[1797, 7692957, 22160670489, 62251231105989, 174870196450697472, 491247081391884320853, 1379941504320192861211113, 3876267907943321538519195237, 10888439667180264563034515970573, 30585627308852919399954121459126272]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.105413.1 |
$D_{4}$ |
simple |
2.53.ax_iw |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 23 x + 230 x^{2} - 1219 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$31$ |
$[31, 2741, 148924, 7890609, 418168331, 22163957066, 1174708119455, 62259680408833, 3299763640178908, 174887471231929421]$ |
$1798$ |
$[1798, 7699036, 22171008544, 62260687509376, 174876111723431998, 491249948520399745792, 1379942713983883886781454, 3876268427364307171623464448, 10888439921414837070026991032608, 30585627442373572700311942608465916]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.814572.2 |
$D_{4}$ |
simple |
2.53.ax_ix |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 23 x + 231 x^{2} - 1219 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$31$ |
$[31, 2743, 148993, 7891803, 418182246, 22164079663, 1174709013649, 62259686667891, 3299763690957319, 174887471709640518]$ |
$1799$ |
$[1799, 7705117, 22181347979, 62270112738869, 174881930871427024, 491252665778871345181, 1379943764401563675482987, 3876268817051269300871884325, 10888440088971592276572517336871, 30585627525919258424418444702161152]$ |
$7$ |
$7$ |
$2$ |
$2$ |
$1$ |
4.0.24389.1 |
$C_4$ |
simple |
2.53.ax_iy |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 14 x + 53 x^{2} )( 1 - 9 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$31$ |
$[31, 2745, 149062, 7892993, 418195931, 22164195510, 1174709773247, 62259690882913, 3299763716578606, 174887471925324225]$ |
$1800$ |
$[1800, 7711200, 22191688800, 62279506800000, 174887653896945000, 491255233433824204800, 1379944656708092760853800, 3876269079477172617892800000, 10888440173515782831172165192800, 30585627563639636518417327289580000]$ |
$15$ |
$15$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-131}) \) |
$C_2$, $C_2$ |
1.53.ao $\times$ 1.53.aj |
2.53.ax_iz |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 23 x + 233 x^{2} - 1219 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$31$ |
$[31, 2747, 149131, 7894179, 418209386, 22164304619, 1174710399215, 62259693093571, 3299763718148563, 174887471902446182]$ |
$1801$ |
$[1801, 7717285, 22202031013, 62288869698325, 174893280802276096, 491257651751798178685, 1379945392038336544719517, 3876269217111994462945251525, 10888440178696268343039675054457, 30585627559638553429735293973196800]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.1222893.1 |
$D_{4}$ |
simple |
2.53.ax_ja |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 23 x + 234 x^{2} - 1219 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$31$ |
$[31, 2749, 149200, 7895361, 418222611, 22164407002, 1174710892519, 62259693339489, 3299763696768016, 174887471664210309]$ |
$1802$ |
$[1802, 7723372, 22212374624, 62298201439424, 174898811589738322, 491259920999348055808, 1379945971527165406336178, 3876269232422724870015064832, 10888440108145515395323181553248, 30585627517974084082995959809773772]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.997628.1 |
$D_{4}$ |
simple |
2.53.ax_jb |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 23 x + 235 x^{2} - 1219 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$31$ |
$[31, 2751, 149269, 7896539, 418235606, 22164502671, 1174711254125, 62259691660243, 3299763653532823, 174887471233559046]$ |
$1803$ |
$[1803, 7729461, 22222719639, 62307502028901, 174904246261677648, 491262041443043727477, 1379946396309454812702399, 3876269127873366612818371653, 10888439965479597558776832054963, 30585627442658573856094128611394816]$ |
$9$ |
$9$ |
$2$ |
$2$ |
$1$ |
4.0.698477.1 |
$D_{4}$ |
simple |
2.53.ax_jc |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 13 x + 53 x^{2} )( 1 - 10 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$31$ |
$[31, 2753, 149338, 7897713, 418248371, 22164591638, 1174711484999, 62259688095361, 3299763589533874, 174887470633173593]$ |
$1804$ |
$[1804, 7735552, 22233066064, 62316771472384, 174909584820468124, 491264013349470355456, 1379946667520085430045852, 3876268905924935251721932800, 10888439754298195405890708638416, 30585627337658680556435299723524352]$ |
$8$ |
$8$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.53.an $\times$ 1.53.ak |
2.53.ax_jd |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 23 x + 237 x^{2} - 1219 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$31$ |
$[31, 2755, 149407, 7898883, 418260906, 22164673915, 1174711586107, 62259682684323, 3299763505857091, 174887469885474150]$ |
$1805$ |
$[1805, 7741645, 22243413905, 62326009775525, 174914827268512000, 491265836985228540805, 1379946786293943236489105, 3876268569035459181589679525, 10888439478184596525487546944005, 30585627206895416397345349923328000]$ |
$5$ |
$5$ |
$2$ |
$2$ |
$1$ |
4.0.137525.1 |
$D_{4}$ |
simple |
2.53.ax_je |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 12 x + 53 x^{2} )( 1 - 11 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$31$ |
$[31, 2757, 149476, 7900049, 418273211, 22164749514, 1174711558415, 62259675466561, 3299763403583428, 174887469012620157]$ |
$1806$ |
$[1806, 7747740, 22253763168, 62335216944000, 174919973608239846, 491267512616934493440, 1379946753765919635899862, 3876268119659979680564928000, 10888439140705695537794830254432, 30585627054244189974655422994880700]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-17}) \), \(\Q(\sqrt{-91}) \) |
$C_2$, $C_2$ |
1.53.am $\times$ 1.53.al |
2.53.aw_ih |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 22 x + 215 x^{2} - 1166 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$32$ |
$[32, 2756, 148922, 7888644, 418144432, 22163835926, 1174708296976, 62259686411908, 3299763646074770, 174887470579914596]$ |
$1837$ |
$[1837, 7739281, 22170650128, 62245187394841, 174866117878063117, 491247263557807854592, 1379942922519846612692677, 3876268801113820294830573993, 10888439940869782093731958700176, 30585627328344349098755654052506641]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.62352.1 |
$D_{4}$ |
simple |
2.53.aw_ii |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 22 x + 216 x^{2} - 1166 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$32$ |
$[32, 2758, 148988, 7889718, 418156092, 22163933638, 1174709046032, 62259692889246, 3299763710802224, 174887471207739318]$ |
$1838$ |
$[1838, 7745332, 22180530014, 62253663613904, 174870993824030398, 491249429253521495956, 1379943802443171388074446, 3876269204390925212079641600, 10888440154455085804305038493566, 30585627438143026887661265255570452]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.2083136.1 |
$D_{4}$ |
simple |
2.53.aw_ij |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 22 x + 217 x^{2} - 1166 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$32$ |
$[32, 2760, 149054, 7890788, 418167532, 22164025230, 1174709680204, 62259697726468, 3299763756360902, 174887471640037800]$ |
$1839$ |
$[1839, 7751385, 22190411196, 62262108603225, 174875777811308919, 491251459306172743440, 1379944547410930765824831, 3876269505554888495773677225, 10888440304787957999344761475164, 30585627513746615115546200710529625]$ |
$14$ |
$14$ |
$2$ |
$2$ |
$1$ |
4.0.2753600.2 |
$D_{4}$ |
simple |
2.53.aw_ik |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 14 x + 53 x^{2} )( 1 - 8 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$32$ |
$[32, 2762, 149120, 7891854, 418178752, 22164110714, 1174710200416, 62259700959646, 3299763783701600, 174887471895827882]$ |
$1840$ |
$[1840, 7757440, 22200293680, 62270522368000, 174880469841857200, 491253353982162279040, 1379945158508616792330160, 3876269706851546500448256000, 10888440395005800804808094881840, 30585627558481095683012620891331200]$ |
$18$ |
$18$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-37}) \) |
$C_2$, $C_2$ |
1.53.ao $\times$ 1.53.ai |
2.53.aw_il |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 22 x + 219 x^{2} - 1166 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$32$ |
$[32, 2764, 149186, 7892916, 418189752, 22164190102, 1174710607592, 62259702624804, 3299763793770362, 174887471993889084]$ |
$1841$ |
$[1841, 7763497, 22210177472, 62278904913449, 174885069917659801, 491255113547903638528, 1379945636821725366481697, 3876269810523747894796784777, 10888440428230335979980284906432, 30585627575630771319095307593153497]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.193088.1 |
$D_{4}$ |
simple |
2.53.aw_im |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 22 x + 220 x^{2} - 1166 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$32$ |
$[32, 2766, 149252, 7893974, 418200532, 22164263406, 1174710902656, 62259702757918, 3299763787508480, 174887471952762846]$ |
$1842$ |
$[1842, 7769556, 22220062578, 62287256244816, 174889578040727442, 491256738269823368052, 1379945983435756334981202, 3876269818811353697769550848, 10888440407567604927000516369186, 30585627568438307556099491850860916]$ |
$20$ |
$20$ |
$2$ |
$2$ |
$1$ |
4.0.2875712.1 |
$D_{4}$ |
simple |
2.53.aw_in |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 22 x + 221 x^{2} - 1166 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$32$ |
$[32, 2768, 149318, 7895028, 418211092, 22164330638, 1174711086532, 62259701394916, 3299763765852494, 174887471790752768]$ |
$1843$ |
$[1843, 7775617, 22229949004, 62295576367369, 174893994213097123, 491258228414361181456, 1379946199436213588745211, 3876269733951237315466929225, 10888440336107968700750362813996, 30585627540104774704556241853357777]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.2488896.4 |
$D_{4}$ |
simple |
2.53.aw_io |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 22 x + 222 x^{2} - 1166 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$32$ |
$[32, 2770, 149384, 7896078, 418221432, 22164391810, 1174711160144, 62259698571678, 3299763729734192, 174887471525924850]$ |
$1844$ |
$[1844, 7781680, 22239836756, 62303865286400, 174898318436832244, 491259584247970118320, 1379946285908605160413076, 3876269558177284578835558400, 10888440216926108019112398498164, 30585627493789689828299349818062000]$ |
$24$ |
$24$ |
$2$ |
$2$ |
$1$ |
4.0.124400.1 |
$D_{4}$ |
simple |
2.53.aw_ip |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 13 x + 53 x^{2} )( 1 - 9 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$32$ |
$[32, 2772, 149450, 7897124, 418231552, 22164446934, 1174711124416, 62259694324036, 3299763680080610, 174887471176107732]$ |
$1845$ |
$[1845, 7787745, 22249725840, 62312123007225, 174902550714022725, 491260806037116702720, 1379946243938443322963805, 3876269293720393782176334825, 10888440053081023273606423215120, 30585627432611058719667732335892225]$ |
$30$ |
$30$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-131}) \) |
$C_2$, $C_2$ |
1.53.an $\times$ 1.53.aj |
2.53.aw_iq |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 22 x + 224 x^{2} - 1166 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$32$ |
$[32, 2774, 149516, 7898166, 418241452, 22164496022, 1174710980272, 62259688687774, 3299763617814032, 174887470758892934]$ |
$1846$ |
$[1846, 7793812, 22259616262, 62320349535184, 174906691046785126, 491261894048281102708, 1379946074611244689446742, 3876268942808475722473116672, 10888439847616034540410830723142, 30585627359645417874837435039856372]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.906048.1 |
$D_{4}$ |
simple |
2.53.aw_ir |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 22 x + 225 x^{2} - 1166 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$32$ |
$[32, 2776, 149582, 7899204, 418251132, 22164539086, 1174710728636, 62259681698628, 3299763543851990, 174887470291635096]$ |
$1847$ |
$[1847, 7799881, 22269508028, 62328544875641, 174910739437262767, 491262848547957290512, 1379945779012530313831127, 3876268507666453739551067753, 10888439603558781591776731749596, 30585627277927876469287409593174441]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.444992.2 |
$D_{4}$ |
simple |
2.53.aw_is |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 12 x + 53 x^{2} )( 1 - 10 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$32$ |
$[32, 2778, 149648, 7900238, 418260592, 22164576138, 1174710370432, 62259673392286, 3299763459107264, 174887469791452218]$ |
$1848$ |
$[1848, 7805952, 22279401144, 62336709033984, 174914695887625848, 491263669802653203456, 1379945358227825792979576, 3876267990516263757073612800, 10888439323921223907842523099576, 30585627190452158333403308939492352]$ |
$16$ |
$16$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-17}) \), \(\Q(\sqrt{-7}) \) |
$C_2$, $C_2$ |
1.53.am $\times$ 1.53.ak |
2.53.aw_it |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 11 x + 53 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$32$ |
$[32, 2780, 149714, 7901268, 418269832, 22164607190, 1174709906584, 62259663804388, 3299763364487882, 174887469275225900]$ |
$1849$ |
$[1849, 7812025, 22289295616, 62344842015625, 174918560400071569, 491264358078890905600, 1379944813342661369750521, 3876267393576854324387015625, 10888439011699640688856675320064, 30585627100170643928223625511775625]$ |
$9$ |
$9$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-91}) \) |
$C_2$ |
1.53.al 2 |
2.53.av_hs |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 200 x^{2} - 1113 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$33$ |
$[33, 2769, 148878, 7886545, 418126173, 22163807958, 1174709005545, 62259690130369, 3299763591802134, 174887469600103689]$ |
$1876$ |
$[1876, 7774144, 22164084544, 62228633193216, 174858482655669316, 491246643673579687936, 1379943754882074103465156, 3876269032623917476904684544, 10888439761782911051000643908416, 30585627156987698388382088492530624]$ |
$8$ |
$8$ |
$4$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}, \sqrt{65})\) |
$C_2^2$ |
simple |
2.53.av_ht |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 201 x^{2} - 1113 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$33$ |
$[33, 2771, 148941, 7887507, 418135938, 22163888099, 1174709688801, 62259697089763, 3299763664516293, 174887470263891686]$ |
$1877$ |
$[1877, 7780165, 22173505913, 62236223991925, 174862566037320272, 491248419924968196205, 1379944557510528029870753, 3876269465913740683994413125, 10888440001722451933365179961317, 30585627273075901982419993520435200]$ |
$7$ |
$7$ |
$2$ |
$2$ |
$1$ |
4.0.2816797.1 |
$D_{4}$ |
simple |
2.53.av_hu |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 202 x^{2} - 1113 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$33$ |
$[33, 2773, 149004, 7888465, 418145493, 22163962714, 1174710274449, 62259702732865, 3299763722378076, 174887470774636813]$ |
$1878$ |
$[1878, 7786188, 22182928488, 62243783504064, 174866561627229438, 491250073696807977216, 1379945245477580325665214, 3876269817251606502253148928, 10888440192652662383788609872552, 30585627362398825268891096482500588]$ |
$18$ |
$18$ |
$2$ |
$2$ |
$1$ |
4.0.90972.2 |
$D_{4}$ |
simple |
2.53.av_hv |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 203 x^{2} - 1113 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$33$ |
$[33, 2775, 149067, 7889419, 418154838, 22164031815, 1174710763371, 62259707092339, 3299763766200561, 174887471147679750]$ |
$1879$ |
$[1879, 7792213, 22192352275, 62251311734469, 174870469427047504, 491251605255382639525, 1379945819819359118863771, 3876270088671166619280259269, 10888440337256507390902520973775, 30585627427639360933628662962742528]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.5587101.2 |
$D_{4}$ |
simple |
2.53.av_hw |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 14 x + 53 x^{2} )( 1 - 7 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$33$ |
$[33, 2777, 149130, 7890369, 418163973, 22164095414, 1174711156449, 62259710200801, 3299763796792290, 174887471398145057]$ |
$1880$ |
$[1880, 7798240, 22201777280, 62258808688000, 174874289438449400, 491253014866986711040, 1379946281571995434938680, 3876270282203084749665216000, 10888440438201984267472113242240, 30585627471442604984620813521311200]$ |
$6$ |
$6$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-163}) \) |
$C_2$, $C_2$ |
1.53.ao $\times$ 1.53.ah |
2.53.av_hx |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 205 x^{2} - 1113 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$33$ |
$[33, 2779, 149193, 7891315, 418172898, 22164153523, 1174711454565, 62259712090819, 3299763814957269, 174887471540941414]$ |
$1881$ |
$[1881, 7804269, 22211203509, 62266274369541, 174878021663134416, 491254302797925784821, 1379946631771623278163141, 3876270399875036662630353189, 10888440498142122656731456689201, 30585627496415898726011812155469824]$ |
$25$ |
$25$ |
$2$ |
$2$ |
$1$ |
4.0.80725.3 |
$D_{4}$ |
simple |
2.53.av_hy |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 206 x^{2} - 1113 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$33$ |
$[33, 2781, 149256, 7892257, 418181613, 22164206154, 1174711658601, 62259712794913, 3299763821494968, 174887471590761861]$ |
$1882$ |
$[1882, 7810300, 22220630968, 62273708784000, 174881666102826322, 491255469314516665600, 1379946871454379713978338, 3876270443711710210353600000, 10888440519714984538999676685112, 30585627505128870732183827353601500]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.6475212.1 |
$D_{4}$ |
simple |
2.53.av_hz |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 207 x^{2} - 1113 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$33$ |
$[33, 2783, 149319, 7893195, 418190118, 22164253319, 1174711769439, 62259712345555, 3299763817200321, 174887471562084038]$ |
$1883$ |
$[1883, 7816333, 22230059663, 62281111936309, 174885222759273488, 491256514683087517021, 1379947001656404952388639, 3876270415734805356979393893, 10888440505543664238584393550587, 30585627500113478821922239448236288]$ |
$13$ |
$13$ |
$2$ |
$2$ |
$1$ |
4.0.50653.1 |
$C_4$ |
simple |
2.53.av_ia |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 208 x^{2} - 1113 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$33$ |
$[33, 2785, 149382, 7894129, 418198413, 22164295030, 1174711787961, 62259710775169, 3299763802863726, 174887471469170425]$ |
$1884$ |
$[1884, 7822368, 22239489600, 62288483831424, 174888691634249004, 491257439169978009600, 1379947023413842432389996, 3876270317963034208326019584, 10888440458236288430978816769600, 30585627483864052032667632926788128]$ |
$36$ |
$36$ |
$2$ |
$2$ |
$1$ |
4.0.1389564.2 |
$D_{4}$ |
simple |
2.53.av_ib |
$2$ |
$\F_{53}$ |
$53$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 21 x + 209 x^{2} - 1113 x^{3} + 2809 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$33$ |
$[33, 2787, 149445, 7895059, 418206498, 22164331299, 1174711715049, 62259708116131, 3299763779271045, 174887471326068582]$ |
$1885$ |
$[1885, 7828405, 22248920785, 62295824474325, 174892072729550800, 491258243041539469405, 1379946937762838907436585, 3876270152412121042297659525, 10888440380386016150358968571805, 30585627458837332594857678053478400]$ |
$16$ |
$16$ |
$2$ |
$2$ |
$1$ |
4.0.4821453.2 |
$D_{4}$ |
simple |
2.53.av_ic |
$2$ |
$\F_{53}$ |
$53$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 13 x + 53 x^{2} )( 1 - 8 x + 53 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$33$ |
$[33, 2789, 149508, 7895985, 418214373, 22164362138, 1174711551585, 62259704400769, 3299763747203604, 174887471146611389]$ |
$1886$ |
$[1886, 7834444, 22258353224, 62303133870016, 174895366047001766, 491258926564135027456, 1379946745739544531950726, 3876269921094802340009481984, 10888440274571038797387586384136, 30585627427452517906362172596428524]$ |
$6$ |
$6$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-37}) \) |
$C_2$, $C_2$ |
1.53.an $\times$ 1.53.ai |