| 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 |
| 2.625.adw_fog |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
|
|
|
✓ |
✓ |
✓ |
$( 1 - 25 x )^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]$ |
$2$ |
$0$ |
$2$ |
$0$ |
$2$ |
$526$ |
$[526, 388126, 244078126, 152586328126, 95367392578126, 59604643798828126, 37252902960205078126, 23283064364776611328126, 14551915228351593017578126, 9094947017728900909423828126]$ |
$331776$ |
$[331776, 151613669376, 59589387451109376, 23282825947723387109376, 9094943292439556121787109376, 3552713620592840373516081787109376, 1387778779871950973980128765081787109376, 542101086228541362288664095103740081787109376, 211758236813353040162155681173317134365081787109376, 82718061255299298040188915647377143613993740081787109376]$ |
$None$ |
$None$ |
$15$ |
$12$ |
$1$ |
\(\Q\) |
Trivial |
1.625.aby 2 |
| 2.625.adv_fmi |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 25 x )^{2}( 1 - 49 x + 625 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$527$ |
$[527, 388225, 244083602, 152586565825, 95367401584127, 59604644111091550, 37252902970365516527, 23283064365091515201025, 14551915228360978209130802, 9094947017729171598283878625]$ |
$332352$ |
$[332352, 151652217600, 59590724194052352, 23282862217526698675200, 9094944151318564946239474752, 3552713639205190684910894599372800, 1387778780250456799889751804783109657152, 542101086235873289430185046325370798302310400, 211758236813489612674032135393014923177567564599552, 82718061255301759941029364420712619518542369687883488000]$ |
$None$ |
$None$ |
$8$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-11}) \) |
Trivial, $C_2$ |
1.625.aby $\times$ 1.625.abx |
| 2.625.adu_fkk |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 25 x )^{2}( 1 - 48 x + 625 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$528$ |
$[528, 388322, 244088784, 152586779710, 95367409155408, 59604644351360162, 37252902977342377104, 23283064365278283219070, 14551915228365572808044688, 9094947017729273653223445602]$ |
$332928$ |
$[332928, 151689987072, 59591989168838784, 23282894853620587560960, 9094944873372040269127905408, 3552713653526315836528393863078912, 1387778780510365110016779969285936127104, 542101086240221821215665538008115583459000320, 211758236813556472887935315819975452425631401794688, 82718061255302688125297623620854173636381426668360164352]$ |
$None$ |
$None$ |
$16$ |
$12$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-1}) \) |
Trivial, $C_2$ |
1.625.aby $\times$ 1.625.abw |
| 2.625.adu_fkl |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
|
✓ |
|
|
✓ |
✓ |
$( 1 - 49 x + 625 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$528$ |
$[528, 388324, 244089078, 152586803524, 95367410590128, 59604644423354974, 37252902980525954928, 23283064365406419073924, 14551915228370363400683478, 9094947017729442287143929124]$ |
$332929$ |
$[332929, 151690775625, 59592060966981904, 23282898487386511055625, 9094945010197654878745852129, 3552713657817541093814153379840000, 1387778780628962625902609352984947641729, 542101086243205216571805161996168304364175625, 211758236813626185185908677694533192411001024850704, 82718061255304221841869813267320554378529632778810015625]$ |
$None$ |
$None$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-11}) \) |
$C_2$ |
1.625.abx 2 |
| 2.625.adt_fim |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 25 x )^{2}( 1 - 47 x + 625 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$529$ |
$[529, 388417, 244093678, 152586970945, 95367415414369, 59604644528963422, 37252902981713628913, 23283064365367799748865, 14551915228366851556454734, 9094947017729271456171660577]$ |
$333504$ |
$[333504, 151726977792, 59593183840124928, 23282924033616449080320, 9094945470272953332640023744, 3552713664112294973059395017244672, 1387778780673206929525437879489281988288, 542101086242306040340621284561503887086858240, 211758236813575081126396704350644278179168450985984, 82718061255302668143228043611353054683575428530146269952]$ |
$None$ |
$None$ |
$8$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-291}) \) |
Trivial, $C_2$ |
1.625.aby $\times$ 1.625.abv |
| 2.625.adt_fin |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 97 x + 3601 x^{2} - 60625 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$529$ |
$[529, 388419, 244093969, 152586994179, 95367416788374, 59604644596356579, 37252902984614088769, 23283064365480931295619, 14551915228370932655500129, 9094947017729409470169161374]$ |
$333505$ |
$[333505, 151727766245, 59593254905124145, 23282927578878967699205, 9094945601308328900003722000, 3552713668129240209344524792228805, 1387778780781257479202795525636673703345, 542101086244940089425493905699926338327175045, 211758236813634468933743894360555893208887431791905, 82718061255303923373223018404102505412827726732197888000]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.242525.2 |
$D_{4}$ |
simple |
| 2.625.adt_fio |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 49 x + 625 x^{2} )( 1 - 48 x + 625 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$529$ |
$[529, 388421, 244094260, 152587017409, 95367418161409, 59604644663623586, 37252902987502815505, 23283064365593187091969, 14551915228374957999597364, 9094947017729544342083496101]$ |
$333506$ |
$[333506, 151728554700, 59593325970144968, 23282931123531240192000, 9094945732251198388598540066, 3552713672138666320458752106393600, 1387778780888870936100525479612747929058, 542101086247553748357344467651129130339328000, 211758236813693045399811901242684636196276418904776, 82718061255305150026138072495087243750276259928699463500]$ |
$None$ |
$None$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-1}) \) |
$C_2$, $C_2$ |
1.625.abx $\times$ 1.625.abw |
| 2.625.ads_fgo |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 25 x )^{2}( 1 - 46 x + 625 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$530$ |
$[530, 388510, 244098290, 152587140670, 95367420477650, 59604644652491230, 37252902983989503410, 23283064365385983576190, 14551915228365979578311570, 9094947017729212351140651550]$ |
$334080$ |
$[334080, 151763189760, 59594309672567040, 23282949931463587921920, 9094945953144959085213446400, 3552713671475126028465738890772480, 1387778780757989861339566093792094972160, 542101086242729415562632792537803191159357440, 211758236813562392174376399740850992152295496280320, 82718061255302130586102535275755088212492586679753932800]$ |
$None$ |
$None$ |
$8$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-6}) \) |
Trivial, $C_2$ |
1.625.aby $\times$ 1.625.abu |
| 2.625.ads_fgp |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 96 x + 3551 x^{2} - 60000 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$530$ |
$[530, 388512, 244098578, 152587163332, 95367421792850, 59604644715526374, 37252902986628985010, 23283064365485718569092, 14551915228369450326745778, 9094947017729325130802729952]$ |
$334081$ |
$[334081, 151763978113, 59594380004433604, 23282953389443494065033, 9094946078572247752125285601, 3552713675232313439523674692790800, 1387778780856318213353534037100883967361, 542101086245051551821881384742752396737449993, 211758236813612898211370000594869234549155590049604, 82718061255303156311153815763672325272882022543262277953]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.1382544.1 |
$D_{4}$ |
simple |
| 2.625.ads_fgq |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 96 x + 3552 x^{2} - 60000 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$530$ |
$[530, 388514, 244098866, 152587185990, 95367423107090, 59604644778438242, 37252902989257171634, 23283064365584625012862, 14551915228372869353694866, 9094947017729435059194895394]$ |
$334082$ |
$[334082, 151764766468, 59594450336321474, 23282956846813150755856, 9094946203907983996969941122, 3552713678982153029098604693041156, 1387778780954225794723640130598183652162, 542101086247354396918361686176019244874989568, 211758236813662651601696652553694565650701898424578, 82718061255304156104056304637839320005935381102361553668]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.1229056.2 |
$D_{4}$ |
simple |
| 2.625.ads_fgr |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 49 x + 625 x^{2} )( 1 - 47 x + 625 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$530$ |
$[530, 388516, 244099154, 152587208644, 95367424420370, 59604644841226846, 37252902991874067314, 23283064365682703621764, 14551915228376236748007410, 9094947017729542145031711076]$ |
$334083$ |
$[334083, 151765554825, 59594520668230656, 23282960303572558079625, 9094946329152167820319683363, 3552713682724645512448755341721600, 1387778781051712755653597224556698107651, 542101086249637967482328403306438358193711625, 211758236813711653638273301774652237911398524679168, 82718061255305130044068492484991407354309930550893591625]$ |
$None$ |
$None$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-291}) \) |
$C_2$, $C_2$ |
1.625.abx $\times$ 1.625.abv |
| 2.625.ads_fgs |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
|
✓ |
|
|
✓ |
✓ |
$( 1 - 48 x + 625 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$530$ |
$[530, 388518, 244099442, 152587231294, 95367425732690, 59604644903892198, 37252902994479676082, 23283064365779955110014, 14551915228379552598511250, 9094947017729646397023063078]$ |
$334084$ |
$[334084, 151766343184, 59594591000161156, 23282963759721716121600, 9094946454304799222747208964, 3552713686459791604832356745353744, 1387778781148779246347118189751444989316, 542101086251902280142918655598654413760102400, 211758236813759905613715145901175259463962656579844, 82718061255306078210406331733269143812042214698857829904]$ |
$None$ |
$None$ |
$16$ |
$12$ |
$1$ |
\(\Q(\sqrt{-1}) \) |
$C_2$ |
1.625.abw 2 |
| 2.625.adr_fer |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 95 x + 3501 x^{2} - 59375 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$531$ |
$[531, 388603, 244102911, 152587312099, 95367425714526, 59604644788740403, 37252902987017026791, 23283064365442149428899, 14551915228366807054134771, 9094947017729222079326246878]$ |
$334657$ |
$[334657, 151799411229, 59595437729566537, 23282976089367302716725, 9094946452572333143055185152, 3552713679596209585298569610152029, 1387778780870773896157574925328902004417, 542101086244037128726421977909571765750847525, 211758236813574433532409168615400859615299001431897, 82718061255302219063435103437595335470496162038459797504]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.4189941.1 |
$D_{4}$ |
simple |
| 2.625.adr_fes |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 95 x + 3502 x^{2} - 59375 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$531$ |
$[531, 388605, 244103196, 152587334193, 95367426971851, 59604644847532242, 37252902989405528571, 23283064365529177931169, 14551915228369707453593196, 9094947017729311640004387565]$ |
$334658$ |
$[334658, 151800199484, 59595507328332704, 23282979460675134555584, 9094946572480227250343736258, 3552713683100476302223288252173056, 1387778780959752521277255835624872081074, 542101086246063418946418302441254616270124800, 211758236813616639899456581077861583981292031970208, 82718061255303033613057664893990781518901298682645667964]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.5492156.1 |
$D_{4}$ |
simple |
| 2.625.adr_fet |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 95 x + 3503 x^{2} - 59375 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$531$ |
$[531, 388607, 244103481, 152587356283, 95367428228226, 59604644906203655, 37252902991783165581, 23283064365615423705139, 14551915228372559996948871, 9094947017729398624138684862]$ |
$334659$ |
$[334659, 151800987741, 59595576927119883, 23282982831372713749989, 9094946692297522593409255344, 3552713686597565070847168467385509, 1387778781048326402175317179832110262643, 542101086248071484853026787712834432445588325, 211758236813658149868553617635423752906773127468179, 82718061255303824729150481864102222449313166531464289536]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.4818021.2 |
$D_{4}$ |
simple |
| 2.625.adr_feu |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 49 x + 625 x^{2} )( 1 - 46 x + 625 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$531$ |
$[531, 388609, 244103766, 152587378369, 95367429483651, 59604644964754654, 37252902994149941811, 23283064365700887449089, 14551915228375364769864246, 9094947017729483040000702049]$ |
$334660$ |
$[334660, 151801776000, 59595646525928080, 23282986201460040384000, 9094946812024219172806855300, 3552713690087476606428315500544000, 1387778781136495687490849321494686450820, 542101086250061342704345637440386431429376000, 211758236813698964686252988981177048543648994666640, 82718061255304592486942984133394367416144175400356400000]$ |
$None$ |
$None$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-6}) \) |
$C_2$, $C_2$ |
1.625.abx $\times$ 1.625.abu |
| 2.625.adr_few |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 48 x + 625 x^{2} )( 1 - 47 x + 625 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$531$ |
$[531, 388613, 244104336, 152587422529, 95367431991651, 59604645081495458, 37252902998850927891, 23283064365869471639809, 14551915228380831346921296, 9094947017729644199971278053]$ |
$334662$ |
$[334662, 151803352524, 59595785723607552, 23282992939803936307200, 9094947051205816042820851302, 3552713697045770839494848747556864, 1387778781311621065930687549113747201702, 542101086253986499267919310078815719954636800, 211758236813778513852176552308478917109885733652992, 82718061255306058228336751722949087428929640002658838604]$ |
$None$ |
$None$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-291}) \) |
$C_2$, $C_2$ |
1.625.abw $\times$ 1.625.abv |
| 2.625.adq_fcs |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 25 x )^{2}( 1 - 44 x + 625 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$532$ |
$[532, 388690, 244106692, 152587420030, 95367427455652, 59604644768186770, 37252902983988092212, 23283064365290456982910, 14551915228361168897272372, 9094947017729046870963322450]$ |
$335232$ |
$[335232, 151833277440, 59596360679544192, 23282992558198463201280, 9094946618618951519263393152, 3552713678371117535770773186155520, 1387778780757937290117397231768167779712, 542101086240505263742717563226670283132764160, 211758236813492387551703315395297058607140576959872, 82718061255300625552657242696468207716534092952506291200]$ |
$None$ |
$None$ |
$8$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-141}) \) |
Trivial, $C_2$ |
1.625.aby $\times$ 1.625.abs |
| 2.625.adq_fct |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 94 x + 3451 x^{2} - 58750 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$532$ |
$[532, 388692, 244106974, 152587441572, 95367428658852, 59604644823202974, 37252902986166993412, 23283064365367693135812, 14551915228363672540637374, 9094947017729122287722688052]$ |
$335233$ |
$[335233, 151834065593, 59596429545179200, 23282995845275515592873, 9094946733365078666128682353, 3552713681650338862283693853516800, 1387778780839107685155321767863812531313, 542101086242303558062080156330817409983315913, 211758236813528820357712888888550378256790187252800, 82718061255301311464087921680783956125262427956573422553]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.601664.1 |
$D_{4}$ |
simple |
| 2.625.adq_fcu |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 94 x + 3452 x^{2} - 58750 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$532$ |
$[532, 388694, 244107256, 152587463110, 95367429861112, 59604644878101542, 37252902988335440308, 23283064365444188968702, 14551915228366131780448756, 9094947017729195363421591494]$ |
$335234$ |
$[335234, 151834853748, 59596498410834914, 23282999131742312029776, 9094946848021560706084093394, 3552713684922548537397791324172756, 1387778780919888627021561399559220144786, 542101086244084615462953756858782048304043008, 211758236813564607006974347534594991213309986416818, 82718061255301976083697732020726539790032277720423925268]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.14742336.1 |
$D_{4}$ |
simple |
| 2.625.adq_fcv |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 94 x + 3453 x^{2} - 58750 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$532$ |
$[532, 388696, 244107538, 152587484644, 95367431062432, 59604644932882486, 37252902990493436848, 23283064365519945164164, 14551915228368546699304882, 9094947017729266105915533976]$ |
$335235$ |
$[335235, 151835641905, 59596567276511340, 23283002417598852594825, 9094946962588397639667003675, 3552713688187747276371046563031440, 1387778781000280262790583994830910260635, 542101086245848451837985588301973125132204425, 211758236813599748701452082296796684763442443821740, 82718061255302619482932040928062381707987031630563919025]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.16248384.1 |
$D_{4}$ |
simple |
| 2.625.adq_fcw |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 94 x + 3454 x^{2} - 58750 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$532$ |
$[532, 388698, 244107820, 152587506174, 95367432262812, 59604644987545818, 37252902992640986980, 23283064365594962404734, 14551915228370917379783812, 9094947017729334523055543578]$ |
$335236$ |
$[335236, 151836430064, 59596636142208484, 23283005702845137370880, 9094947077065589467415204836, 3552713691445935794461443973380464, 1387778781080282739536857440222428501764, 542101086247595083078705287136302963691089920, 211758236813634246642815022051958454081011265338756, 82718061255303241733195532825154572337319874560784353904]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.940400.1 |
$D_{4}$ |
simple |
| 2.625.adq_fcy |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 94 x + 3456 x^{2} - 58750 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$532$ |
$[532, 388702, 244108384, 152587549222, 95367434660752, 59604645096519694, 37252902996904763812, 23283064365742782751102, 14551915228375526355820804, 9094947017729464412655512302]$ |
$335238$ |
$[335238, 151838006388, 59596773873664950, 23283012271506939887568, 9094947305751037807560718278, 3552713697941285029025620128513300, 1387778781239120804259028520524703737398, 542101086251036793717738897805538910981485568, 211758236813701316071394921615565104395922813606550, 82718061255304423072225402427767423298134376160192534228]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.8126784.1 |
$D_{4}$ |
simple |
| 2.625.adq_fcz |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 94 x + 3457 x^{2} - 58750 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$532$ |
$[532, 388704, 244108666, 152587570740, 95367435858312, 59604645150830262, 37252902999020998408, 23283064365815587221732, 14551915228377764816433466, 9094947017729525900795164144]$ |
$335239$ |
$[335239, 151838794553, 59596842739424284, 23283015554922457794041, 9094947419959294321035686119, 3552713701178447176015384894145936, 1387778781317956686383862021583405766551, 542101086252731904893524147516277936057745833, 211758236813733889960472428744809317178403170798748, 82718061255304982303597754676083188528868656040454968393]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.4214336.1 |
$D_{4}$ |
simple |
| 2.625.adq_fda |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 48 x + 625 x^{2} )( 1 - 46 x + 625 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$532$ |
$[532, 388706, 244108948, 152587592254, 95367437054932, 59604645205023266, 37252903001126802388, 23283064365887655467134, 14551915228379959368778132, 9094947017729585094940269026]$ |
$335240$ |
$[335240, 151839582720, 59596911605204360, 23283018837727720243200, 9094947534077905730831256200, 3552713704408601963154263877941760, 1387778781396403997783818105108054549640, 542101086254409874489939940370153755954380800, 211758236813765824900156235508613898228490788065160, 82718061255305520671211243365320087123033332751363545600]$ |
$None$ |
$None$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-6}) \) |
$C_2$, $C_2$ |
1.625.abw $\times$ 1.625.abu |
| 2.625.adq_fdb |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
|
✓ |
|
|
✓ |
✓ |
$( 1 - 47 x + 625 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$532$ |
$[532, 388708, 244109230, 152587613764, 95367438250612, 59604645259098718, 37252903003222179700, 23283064365958988169604, 14551915228382110095331342, 9094947017729642002919493028]$ |
$335241$ |
$[335241, 151840370889, 59596980471005184, 23283022119922727318025, 9094947648106872037487293161, 3552713707631750105700258712387584, 1387778781474462885533364750853735186569, 542101086256070718392927977768083565271913225, 211758236813797122090637960350980070950981764448256, 82718061255306038246267171712633858082363146845274097929]$ |
$None$ |
$None$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-291}) \) |
$C_2$ |
1.625.abv 2 |
| 2.625.adp_fau |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
|
$( 1 - 25 x )^{2}( 1 - 43 x + 625 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$533$ |
$[533, 388777, 244110494, 152587531825, 95367429575933, 59604644774140702, 37252902982437858269, 23283064365208499733025, 14551915228358404961868158, 9094947017728977298536956377]$ |
$335808$ |
$[335808, 151867153152, 59597288783391744, 23283009616674355891200, 9094946820824663433943247808, 3552713678725999534740410887421952, 1387778780700186575454278387229264030144, 542101086238597047818460016332084782474342400, 211758236813452166998004532485783450350897637649408, 82718061255299992795125548404012117191528778171339690752]$ |
$None$ |
$None$ |
$8$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-651}) \) |
Trivial, $C_2$ |
1.625.aby $\times$ 1.625.abr |
| 2.625.adp_fav |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 93 x + 3401 x^{2} - 58125 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$533$ |
$[533, 388779, 244110773, 152587552819, 95367430725878, 59604644825479419, 37252902984414752573, 23283064365276388948579, 14551915228360532288329133, 9094947017729039279933977374]$ |
$335809$ |
$[335809, 151867941205, 59597356915927849, 23283012820131164007045, 9094946930491993889524783504, 3552713681786025548907853028325445, 1387778780773831627186274488925231728249, 542101086240177716793923276130897603448926405, 211758236813483123672327698614003491421023283556609, 82718061255300556512647539208007768581206708590141952000]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.232525.1 |
$D_{4}$ |
simple |
| 2.625.adp_faw |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 93 x + 3402 x^{2} - 58125 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$533$ |
$[533, 388781, 244111052, 152587573809, 95367431874893, 59604644876703266, 37252902986381595437, 23283064365343578996769, 14551915228362618519898028, 9094947017729099142926119901]$ |
$335810$ |
$[335810, 151868729260, 59597425048484360, 23283016022977712992000, 9094947040070632896633300050, 3552713684839204778072524355034880, 1387778780847102233599970753057210031890, 542101086241742107010649500028607661036928000, 211758236813513482337264998965236754469905326869640, 82718061255301100963389398229275802781041924129419688300]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.31273324.1 |
$D_{4}$ |
simple |
| 2.625.adp_fax |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 93 x + 3403 x^{2} - 58125 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$533$ |
$[533, 388783, 244111331, 152587594795, 95367433022978, 59604644927812255, 37252902988338390767, 23283064365410070544627, 14551915228364663736168521, 9094947017729156894965536958]$ |
$335811$ |
$[335811, 151869517317, 59597493181061283, 23283019225214002927701, 9094947149560580455789122096, 3552713687885537937492289054833309, 1387778780919998540205212600740905673779, 542101086243290233999187692782045805794918213, 211758236813543244151056888538462529505175047739179, 82718061255301626215128062170876309882223692158380133632]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.38207421.1 |
$D_{4}$ |
simple |
| 2.625.adp_fay |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 93 x + 3404 x^{2} - 58125 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$533$ |
$[533, 388785, 244111610, 152587615777, 95367434170133, 59604644978806398, 37252902990285142469, 23283064365475864259137, 14551915228366668016714202, 9094947017729212543500008625]$ |
$335812$ |
$[335812, 151870305376, 59597561313658624, 23283022426840033895808, 9094947258961836567512982532, 3552713690925025742425014646841344, 1387778780992520692511845470737038473028, 542101086244822113288969272127315005757838848, 211758236813572410271651503459764619979749293821696, 82718061255302132335600696260157150249487961486466612576]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.10132056.2 |
$D_{4}$ |
simple |
| 2.625.adp_fba |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 49 x + 625 x^{2} )( 1 - 44 x + 625 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$533$ |
$[533, 388789, 244112168, 152587657729, 95367436461653, 59604645080450194, 37252902994148530613, 23283064365605360855809, 14551915228370554088825048, 9094947017729317559823372949]$ |
$335814$ |
$[335814, 151871881500, 59597697578914584, 23283028828261319256000, 9094947477498274450749792054, 3552713696983468149860835257856000, 1387778781136443116268666121080408643974, 542101086247837190884400326435064803815264000, 211758236813628960063579859486460063298823237552344, 82718061255303087453497691509313846358017174372166537500]$ |
$None$ |
$None$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-141}) \) |
$C_2$, $C_2$ |
1.625.abx $\times$ 1.625.abs |
| 2.625.adp_fbb |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 93 x + 3407 x^{2} - 58125 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$533$ |
$[533, 388791, 244112447, 152587678699, 95367437606018, 59604645131099871, 37252902996065174867, 23283064365669065071699, 14551915228372436039436953, 9094947017729366942485963326]$ |
$335815$ |
$[335815, 151872669565, 59597765711573215, 23283032028056573811525, 9094947586633456223306249200, 3552713700002424182879681996343445, 1387778781207843678738544867392983707735, 542101086249320420243324701767531285247786725, 211758236813656346049348278479550398161978535260535, 82718061255303536586197545390409858350584249772445267200]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.28730709.1 |
$D_{4}$ |
simple |
| 2.625.adp_fbc |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 93 x + 3408 x^{2} - 58125 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$533$ |
$[533, 388793, 244112726, 152587699665, 95367438749453, 59604645181634750, 37252902997971791117, 23283064365732074121697, 14551915228374277372417526, 9094947017729414251391004233]$ |
$335816$ |
$[335816, 151873457632, 59597833844252288, 23283035227241569726336, 9094947695679946550517761096, 3552713703014537722442993070905344, 1387778781278870668949196567997367502344, 542101086250787464010042264432116780453682688, 211758236813683140970788778596112531331985401151104, 82718061255303966858182359227201090402217214280194782432]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.5380024.1 |
$D_{4}$ |
simple |
| 2.625.adp_fbd |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 93 x + 3409 x^{2} - 58125 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$533$ |
$[533, 388795, 244113005, 152587720627, 95367439891958, 59604645232054843, 37252902999868383269, 23283064365794388672547, 14551915228376078167239917, 9094947017729459493964414750]$ |
$335817$ |
$[335817, 151874245701, 59597901976951809, 23283038425816307082213, 9094947804637745432907103632, 3552713706019809483808652696611509, 1387778781349524232410466750244266478913, 542101086252238337708396497063652780687826693, 211758236813709345984387901597764197868971520469881, 82718061255304378336990473610283561270652141291485515776]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.1573221.2 |
$D_{4}$ |
simple |
| 2.625.adp_fbf |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 93 x + 3411 x^{2} - 58125 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$533$ |
$[533, 388799, 244113563, 152587762539, 95367442174178, 59604645332550719, 37252903003631510903, 23283064365916936943539, 14551915228379558460202313, 9094947017729543809798163774]$ |
$335819$ |
$[335819, 151875821845, 59598038242412219, 23283044821135006444405, 9094948022287268865312429104, 3552713712009830532978571196925805, 1387778781489711661124244758048352445499, 542101086255091636989800967668164530522154245, 211758236813759990912546588938353185840713129042979, 82718061255305145185031176665551047388810378803599648000]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.2560525.1 |
$D_{4}$ |
simple |
| 2.625.adp_fbg |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 47 x + 625 x^{2} )( 1 - 46 x + 625 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$533$ |
$[533, 388801, 244113842, 152587783489, 95367443313893, 59604645382626526, 37252903005498054197, 23283064365977171996929, 14551915228381238117188178, 9094947017729582897888484001]$ |
$335820$ |
$[335820, 151876609920, 59598106375173120, 23283048017878968614400, 9094948130978993416376009100, 3552713714994581251298615244226560, 1387778781559245817396443727360110749580, 542101086256494093614950235812542126769305600, 211758236813784433138617642436074387903758455034880, 82718061255305500689141663355134714590349180341217225600]$ |
$None$ |
$None$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-291}) \), \(\Q(\sqrt{-6}) \) |
$C_2$, $C_2$ |
1.625.abv $\times$ 1.625.abu |
| 2.625.ado_eyw |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
|
✓ |
|
✓ |
✓ |
$( 1 - 25 x )^{2}( 1 - 42 x + 625 x^{2} )$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$1$ |
$1$ |
$534$ |
$[534, 388862, 244114038, 152587626430, 95367430911894, 59604644753656382, 37252902980255509878, 23283064365119618051710, 14551915228355909186373654, 9094947017728928844467250302]$ |
$336384$ |
$[336384, 151900250112, 59598153907020288, 23283024052177838407680, 9094946948231806682997318144, 3552713677505038927677090554437632, 1387778780618887762592355702943634416128, 542101086236527609911526184116318549793832960, 211758236813415848684579493959383319153333502779904, 82718061255299552107928778299666734512092522899643031552]$ |
$None$ |
$None$ |
$8$ |
$6$ |
$1$ |
\(\Q\), \(\Q(\sqrt{-46}) \) |
Trivial, $C_2$ |
1.625.aby $\times$ 1.625.abq |
| 2.625.ado_eyx |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 92 x + 3351 x^{2} - 57500 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$534$ |
$[534, 388864, 244114314, 152587646884, 95367432010374, 59604644801528134, 37252902982047725814, 23283064365179278167364, 14551915228357720097033034, 9094947017728980147058390624]$ |
$336385$ |
$[336385, 151901038065, 59598221306468740, 23283027173235188647785, 9094947052991048445719364625, 3552713680358417719217090833161360, 1387778780685653008992078032040952329265, 542101086237916680224343607317782193273166665, 211758236813442200902980930816822681075467242885060, 82718061255300018702277071747682504365333154141673036625]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.33123600.1 |
$D_{4}$ |
simple |
| 2.625.ado_eyy |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 92 x + 3352 x^{2} - 57500 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$534$ |
$[534, 388866, 244114590, 152587667334, 95367433107934, 59604644849287746, 37252902983830281750, 23283064365238278375294, 14551915228359493003394934, 9094947017729029534299309826]$ |
$336386$ |
$[336386, 151901826020, 59598288705937298, 23283030293682276630800, 9094947157662552418964888466, 3552713683205112446386194305772260, 1387778780752058392349732672612450530178, 542101086239290385863148871578522095147827200, 211758236813468000086067126038063183318733958001346, 82718061255300467876616583714006604835189433125970544100]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.57714944.1 |
$D_{4}$ |
simple |
| 2.625.ado_eyz |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 92 x + 3353 x^{2} - 57500 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$534$ |
$[534, 388868, 244114866, 152587687780, 95367434204574, 59604644896935230, 37252902985603181550, 23283064365296619327172, 14551915228361227982127186, 9094947017729077013255607908]$ |
$336387$ |
$[336387, 151902613977, 59598356105425968, 23283033413519102437161, 9094947262246318603237424067, 3552713686045123824442152274608384, 1387778780818104056610542627104743218787, 542101086240648742000863111413101593351397833, 211758236813493247349501871654776710279896062964144, 82718061255300899695208571847146296575064435869964222457]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.4665921.1 |
$D_{4}$ |
simple |
| 2.625.ado_eza |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 92 x + 3354 x^{2} - 57500 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$534$ |
$[534, 388870, 244115142, 152587708222, 95367435300294, 59604644944470598, 37252902987366429078, 23283064365354301674622, 14551915228362925109877750, 9094947017729122590988610950]$ |
$336388$ |
$[336388, 151903401936, 59598423504934756, 23283036532745666147328, 9094947366742346999040908068, 3552713688878452568642719268923344, 1387778780883790145719730914717235385412, 542101086241991763809289874310393958475972608, 211758236813517943808659784039408566678090821119044, 82718061255301314222275422719651299140353366898570189776]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.1325376.2 |
$D_{4}$ |
simple |
| 2.625.ado_ezc |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 92 x + 3356 x^{2} - 57500 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$534$ |
$[534, 388874, 244115694, 152587749094, 95367437488974, 59604645039205034, 37252902990863982774, 23283064365467693162494, 14551915228366206118926294, 9094947017729208071008668074]$ |
$336390$ |
$[336390, 151904977860, 59598558304012710, 23283042769368007601040, 9094947575471190427258479750, 3552713694525065016508714600065540, 1387778781014084174264134650005716175910, 542101086244631865119907224121059388139868160, 211758236813565688774197696306079810457411633076390, 82718061255302091658528916689892130663872284773070906500]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.88377600.1 |
$D_{4}$ |
simple |
| 2.625.ado_ezd |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 49 x + 625 x^{2} )( 1 - 43 x + 625 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$534$ |
$[534, 388876, 244115970, 152587769524, 95367438581934, 59604645086404126, 37252902992598296670, 23283064365523403605924, 14551915228367790153420834, 9094947017729247987397006876]$ |
$336391$ |
$[336391, 151905765825, 59598625703581888, 23283045886763785505625, 9094947679704005460682452991, 3552713697338350150689668151705600, 1387778781078692401589796220056514049263, 542101086245928974960116970885078365534475625, 211758236813588739509881050636883247271221964865216, 82718061255302454695965997198025275049032278585159616625]$ |
$None$ |
$None$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-651}) \) |
$C_2$, $C_2$ |
1.625.abx $\times$ 1.625.abr |
| 2.625.ado_eze |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 92 x + 3358 x^{2} - 57500 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$534$ |
$[534, 388878, 244116246, 152587789950, 95367439673974, 59604645133491150, 37252902994322973750, 23283064365578458050942, 14551915228369336643326806, 9094947017729286030764620558]$ |
$336392$ |
$[336392, 151906553792, 59598693103171208, 23283049003549301636096, 9094947783849082707657145992, 3552713700144955512046281163281344, 1387778781142941629544728368024316818952, 542101086247210811147077560413402725441323008, 211758236813611243899894280633134526596552785938184, 82718061255302800698378819631892934879816386290295581632]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.1178624.1 |
$D_{4}$ |
simple |
| 2.625.ado_ezf |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 92 x + 3359 x^{2} - 57500 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$534$ |
$[534, 388880, 244116522, 152587810372, 95367440765094, 59604645180466118, 37252902996038017878, 23283064365632857148932, 14551915228370845665192810, 9094947017729322208151469200]$ |
$336393$ |
$[336393, 151907341761, 59598760502780676, 23283052119724556073033, 9094947887906422168688508393, 3552713702944881815836324334845584, 1387778781206832002074154197226089512297, 542101086248477388847004605068707180036137353, 211758236813633203058166124371156635777878191648324, 82718061255303129729795447926066427326840902426866497601]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.7219856.1 |
$D_{4}$ |
simple |
| 2.625.ado_ezh |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 92 x + 3361 x^{2} - 57500 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$534$ |
$[534, 388884, 244117074, 152587851204, 95367442944574, 59604645274079934, 37252902999439222734, 23283064365739691909124, 14551915228373751610899954, 9094947017729388993121349524]$ |
$336395$ |
$[336395, 151908917705, 59598895302060080, 23283058350244280188745, 9094948095757887734947054875, 3552713708524700111747800167614720, 1387778781333536756637379397094815395355, 542101086250964829445032574087166264362023305, 211758236813675490133754727081694320139854753087920, 82718061255303737135558090120234366669712312758437847625]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.2533025.1 |
$D_{4}$ |
simple |
| 2.625.ado_ezi |
$2$ |
$\F_{5^{4}}$ |
$5$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 48 x + 625 x^{2} )( 1 - 44 x + 625 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$534$ |
$[534, 388886, 244117350, 152587871614, 95367444032934, 59604645320718806, 37252903001125391190, 23283064365792128873854, 14551915228375148687738934, 9094947017729419614762939926]$ |
$336396$ |
$[336396, 151909705680, 59598962701730028, 23283061464588750028800, 9094948199552013841188153516, 3552713711304593534384790445644240, 1387778781396351426561625058962084201548, 542101086252185722669976788052334631924531200, 211758236813695820277483083910747035232560438447436, 82718061255304015637765950724351496568052393796752552400]$ |
$None$ |
$None$ |
$8$ |
$4$ |
$1$ |
\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-141}) \) |
$C_2$, $C_2$ |
1.625.abw $\times$ 1.625.abs |
| 2.625.ado_ezj |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 92 x + 3363 x^{2} - 57500 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$534$ |
$[534, 388888, 244117626, 152587892020, 95367445120374, 59604645367245670, 37252903002801942150, 23283064365843913096612, 14551915228376508602533626, 9094947017729448398540883208]$ |
$336397$ |
$[336397, 151910493657, 59599030101420148, 23283064578322958497881, 9094948303258402163513750917, 3552713714077810760486326122149904, 1387778781458807816841256984511310301717, 542101086253391418061574036348813205112835433, 211758236813715609642293250194646288882360525305524, 82718061255304277424701314962594398935886188654410858057]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.17246736.2 |
$D_{4}$ |
simple |
| 2.625.ado_ezk |
$2$ |
$\F_{5^{4}}$ |
$5$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 92 x + 3364 x^{2} - 57500 x^{3} + 390625 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$534$ |
$[534, 388890, 244117902, 152587912422, 95367446206894, 59604645413660538, 37252903004468879478, 23283064365895045228542, 14551915228377831431733270, 9094947017729475351473779450]$ |
$336398$ |
$[336398, 151911281636, 59599097501130446, 23283067691446905676688, 9094948406877052702431812718, 3552713716844352505310194128418724, 1387778781520906071421498361767912707182, 542101086254581930780451996216848915678466048, 211758236813734859340668085713610520291389144793454, 82718061255304522560197978701238161149922543438717904676]$ |
$None$ |
$None$ |
$2$ |
$2$ |
$1$ |
4.0.8255744.2 |
$D_{4}$ |
simple |
