| 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 |
| 2.31.aw_hb |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 11 x + 31 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$10$ |
$[10, 844, 29176, 920404, 28613950, 887433118, 27512309170, 852889870564, 26439618778216, 819628285947004]$ |
$441$ |
$[441, 815409, 869306256, 850015773369, 819193181645601, 787600160998560000, 756935545547496412881, 727422126529443458724009, 699053530568242162937669136, 671790527971753837735721993409]$ |
$0$ |
$0$ |
$24$ |
$12$ |
$1$ |
\(\Q(\sqrt{-3}) \) |
$C_2$ |
1.31.al 2 |
| 2.31.av_gq |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 11 x + 31 x^{2} )( 1 - 10 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$11$ |
$[11, 865, 29414, 922441, 28628501, 887523082, 27512793011, 852892072561, 26439626382554, 819628295419705]$ |
$462$ |
$[462, 834372, 876323448, 851893812000, 819609653834202, 787680001205697600, 756948857204449255962, 727424004591664501968000, 699053731624052804308517208, 671790535735847526550622405412]$ |
$0$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-6}) \) |
$C_2$, $C_2$ |
1.31.al $\times$ 1.31.ak |
| 2.31.au_gf |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 11 x + 31 x^{2} )( 1 - 9 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$12$ |
$[12, 884, 29592, 923524, 28632252, 887516318, 27512561172, 852889864324, 26439612076872, 819628229210804]$ |
$483$ |
$[483, 851529, 881571600, 852892297929, 819717013272003, 787673998369440000, 756942478742854868163, 727422121207407025745289, 699053353387250167751936400, 671790481469159451262428604809]$ |
$1$ |
$1$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.31.al $\times$ 1.31.aj |
| 2.31.au_gg |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 10 x + 31 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$12$ |
$[12, 886, 29652, 924478, 28643052, 887613046, 27513276852, 852894274558, 26439633986892, 819628304892406]$ |
$484$ |
$[484, 853776, 883397284, 853776000000, 820026337754404, 787759849506356496, 756962169095504212324, 727425882658734336000000, 699053932679921271635783524, 671790543499941305097587052816]$ |
$3$ |
$3$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-6}) \) |
$C_2$ |
1.31.ak 2 |
| 2.31.at_fu |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 11 x + 31 x^{2} )( 1 - 8 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$13$ |
$[13, 901, 29716, 923881, 28629703, 887474158, 27512254993, 852888622321, 26439612222076, 819628277267101]$ |
$504$ |
$[504, 866880, 885227616, 853221438720, 819644056938504, 787636582701696000, 756934055004862088424, 727421061914904482657280, 699053357226388818397082976, 671790520857459815172830952000]$ |
$2$ |
$2$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-15}) \) |
$C_2$, $C_2$ |
1.31.al $\times$ 1.31.ai |
| 2.31.at_fv |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 19 x + 151 x^{2} - 589 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$13$ |
$[13, 903, 29773, 924723, 28638348, 887542563, 27512689903, 852890868723, 26439621574123, 819628308589198]$ |
$505$ |
$[505, 869105, 886957255, 854000824205, 819891613750000, 787697292957691505, 756946020465749517355, 727422977847709490958005, 699053604490867701741852205, 671790546529934495318820000000]$ |
$3$ |
$3$ |
$10$ |
$10$ |
$1$ |
\(\Q(\zeta_{5})\) |
$C_4$ |
simple |
| 2.31.at_fw |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 10 x + 31 x^{2} )( 1 - 9 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$13$ |
$[13, 905, 29830, 925561, 28646803, 887606282, 27513045013, 852892066321, 26439619681210, 819628238683505]$ |
$506$ |
$[506, 871332, 888687800, 854776692000, 820133751773006, 787753846061582400, 756955790521736610926, 727423999269614328528000, 699053554443009849837954200, 671790489233252602632270540612]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-43}) \) |
$C_2$, $C_2$ |
1.31.ak $\times$ 1.31.aj |
| 2.31.as_fj |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 11 x + 31 x^{2} )( 1 - 7 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$14$ |
$[14, 916, 29792, 923716, 28624274, 887433118, 27512130254, 852889228036, 26439622160672, 819628336307476]$ |
$525$ |
$[525, 880425, 887468400, 853069314825, 819488670538125, 787600160998560000, 756930623127909451725, 727421578523445829084425, 699053619999095057531343600, 671790569248621208609088035625]$ |
$6$ |
$6$ |
$24$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.31.al $\times$ 1.31.ah |
| 2.31.as_fk |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 140 x^{2} - 558 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$14$ |
$[14, 918, 29846, 924454, 28631114, 887480934, 27512398130, 852890533630, 26439628750670, 819628377477318]$ |
$526$ |
$[526, 882628, 889102534, 853751942352, 819684504550006, 787642596554384932, 756937993013063559454, 727422692050580577113088, 699053794236145736561446654, 671790602992590312980871445348]$ |
$2$ |
$2$ |
$2$ |
$2$ |
$1$ |
4.0.90432.3 |
$D_{4}$ |
simple |
| 2.31.as_fl |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 18 x + 141 x^{2} - 558 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$14$ |
$[14, 920, 29900, 925188, 28637774, 887524598, 27512600738, 852891057604, 26439627794708, 819628357987640]$ |
$527$ |
$[527, 884833, 890737508, 854431022953, 819875200202207, 787681348160969488, 756943567244364995903, 727423138941707584087497, 699053768960834198240625188, 671790587018297939982488797633]$ |
$3$ |
$3$ |
$2$ |
$2$ |
$1$ |
4.0.66112.2 |
$D_{4}$ |
simple |
| 2.31.as_fm |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 10 x + 31 x^{2} )( 1 - 8 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$14$ |
$[14, 922, 29954, 925918, 28644254, 887564122, 27512738834, 852890824318, 26439619826414, 819628286739802]$ |
$528$ |
$[528, 887040, 892373328, 855106560000, 820060758349008, 787716426600956160, 756947366635601877648, 727422939974376898560000, 699053558282149604663395728, 671790528621553421765605536000]$ |
$8$ |
$8$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-15}) \) |
$C_2$, $C_2$ |
1.31.ak $\times$ 1.31.ai |
| 2.31.as_fn |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 9 x + 31 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$14$ |
$[14, 924, 30008, 926644, 28650554, 887599518, 27512813174, 852889858084, 26439605375528, 819628172474604]$ |
$529$ |
$[529, 889249, 894010000, 855778556889, 820241179861609, 787747842662560000, 756949412001718331449, 727422115885370631704169, 699053176206303080577610000, 671790434966568283785525656209]$ |
$2$ |
$2$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-43}) \) |
$C_2$ |
1.31.aj 2 |
| 2.31.ar_ey |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 11 x + 31 x^{2} )( 1 - 6 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$15$ |
$[15, 929, 29826, 923209, 28618425, 887411018, 27512214255, 852890748529, 26439629905566, 819628333950329]$ |
$546$ |
$[546, 892164, 888470856, 852601879584, 819321263086326, 787580547946920000, 756932934202199757366, 727422875337410907467904, 699053824771152993605362536, 671790567316636852055558470884]$ |
$2$ |
$2$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-22}) \) |
$C_2$, $C_2$ |
1.31.al $\times$ 1.31.ag |
| 2.31.ar_ez |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 17 x + 129 x^{2} - 527 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$15$ |
$[15, 931, 29877, 923851, 28623780, 887444503, 27512392755, 852891761251, 26439636995637, 819628386019726]$ |
$547$ |
$[547, 894345, 890010025, 853195292205, 819474555124912, 787610264227484625, 756937845150057662197, 727423739079073116887445, 699054012230021287135843975, 671790609994189980882837408000]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.284445.1 |
$D_{4}$ |
simple |
| 2.31.ar_fa |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 17 x + 130 x^{2} - 527 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$15$ |
$[15, 933, 29928, 924489, 28628965, 887474334, 27512518419, 852892198065, 26439639044664, 819628400900893]$ |
$548$ |
$[548, 896528, 891549968, 853785131072, 819622990306908, 787636738032910592, 756941302446906503852, 727424111633216448489728, 699054066405535830403267472, 671790622191216204756454994448]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.74273.1 |
$D_{4}$ |
simple |
| 2.31.ar_fb |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 17 x + 131 x^{2} - 527 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$15$ |
$[15, 935, 29979, 925123, 28633980, 887500523, 27512591961, 852892080499, 26439636489921, 819628385299790]$ |
$549$ |
$[549, 898713, 893090691, 854371399293, 819766569340944, 787659980108871753, 756943325745211971999, 727424011361374821332757, 699053998859072624008824129, 671790609404109997128926155008]$ |
$5$ |
$5$ |
$2$ |
$2$ |
$1$ |
4.0.26533.1 |
$D_{4}$ |
simple |
| 2.31.ar_fc |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 10 x + 31 x^{2} )( 1 - 7 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$15$ |
$[15, 937, 30030, 925753, 28638825, 887523082, 27512614095, 852891430033, 26439629765010, 819628345780177]$ |
$550$ |
$[550, 900900, 894632200, 854954100000, 819905292951250, 787680001205697600, 756943934698295398450, 727423456584252027600000, 699053821054931420240885800, 671790577012715374473681922500]$ |
$7$ |
$7$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.31.ak $\times$ 1.31.ah |
| 2.31.ar_fd |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 17 x + 133 x^{2} - 527 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$15$ |
$[15, 939, 30081, 926379, 28643500, 887542023, 27512585535, 852890268099, 26439619299861, 819628288763854]$ |
$551$ |
$[551, 903089, 896174501, 855533236349, 820039161877776, 787696812078467225, 756943148960368341641, 727422465581729745118709, 699053544360337037967891491, 671790530280522769603285987584]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.54725.1 |
$D_{4}$ |
simple |
| 2.31.ar_fe |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 9 x + 31 x^{2} )( 1 - 8 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$15$ |
$[15, 941, 30132, 927001, 28648005, 887557358, 27512506995, 852888616081, 26439605520732, 819628220530901]$ |
$552$ |
$[552, 905280, 897717600, 856108811520, 820168176876312, 787710423487104000, 756940988186567831352, 727421056592875838714880, 699053180045440758160802400, 671790474354865921164250152000]$ |
$0$ |
$0$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-15}) \) |
$C_2$, $C_2$ |
1.31.aj $\times$ 1.31.ai |
| 2.31.aq_en |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 11 x + 31 x^{2} )( 1 - 5 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$16$ |
$[16, 940, 29824, 922516, 28613776, 887412382, 27512422576, 852891995236, 26439629386624, 819628283271580]$ |
$567$ |
$[567, 902097, 888411888, 851962959225, 819188201495727, 787581758453817600, 756938665625721272127, 727423938641910146186025, 699053811050523467951154288, 671790525778900649051320773537]$ |
$7$ |
$7$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.31.al $\times$ 1.31.af |
| 2.31.aq_eo |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 16 x + 118 x^{2} - 496 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$16$ |
$[16, 942, 29872, 923070, 28617936, 887436462, 27512561008, 852892990974, 26439637120912, 819628334086702]$ |
$568$ |
$[568, 904256, 889856632, 852474684416, 819307268864248, 787603128109496384, 756942474243955623352, 727424787899611908030464, 699054015542242390545850552, 671790567428412315960612442176]$ |
$14$ |
$14$ |
$2$ |
$2$ |
$1$ |
4.0.10496.2 |
$D_{4}$ |
simple |
| 2.31.aq_ep |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 16 x + 119 x^{2} - 496 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$16$ |
$[16, 944, 29920, 923620, 28621936, 887457350, 27512657104, 852893565508, 26439641447584, 819628360580624]$ |
$569$ |
$[569, 906417, 891302084, 852982811433, 819421761855209, 787621664990991888, 756945118078615898441, 727425277915316711016393, 699054129937856647028719556, 671790589143580916034574781457]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.88592.1 |
$D_{4}$ |
simple |
| 2.31.aq_eq |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 16 x + 120 x^{2} - 496 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$16$ |
$[16, 946, 29968, 924166, 28625776, 887475058, 27512711536, 852893737726, 26439642721168, 819628367744626]$ |
$570$ |
$[570, 908580, 892748250, 853487343120, 819531681044250, 787637379813934500, 756946615622602427130, 727425424798572996526080, 699054163610949277285088250, 671790595015400107259000014500]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.794880.1 |
$D_{4}$ |
simple |
| 2.31.aq_er |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 16 x + 121 x^{2} - 496 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$16$ |
$[16, 948, 30016, 924708, 28629456, 887489598, 27512724976, 852893526468, 26439641292736, 819628360444948]$ |
$571$ |
$[571, 910745, 894195136, 853988282345, 819637027021291, 787650283297771520, 756946985369424489931, 727425244618054331817545, 699054125843732444679295936, 671790589032377409130623965625]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.43625.1 |
$D_{4}$ |
simple |
| 2.31.aq_es |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 10 x + 31 x^{2} )( 1 - 6 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$16$ |
$[16, 950, 30064, 925246, 28632976, 887500982, 27512698096, 852892950526, 26439637509904, 819628343423030]$ |
$572$ |
$[572, 912912, 895642748, 854485632000, 819737800390652, 787660386165853200, 756946245813228831932, 727424753401565227008000, 699054025827048251106654908, 671790575080730995591603613712]$ |
$16$ |
$16$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-22}) \) |
$C_2$, $C_2$ |
1.31.ak $\times$ 1.31.ag |
| 2.31.aq_et |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 16 x + 123 x^{2} - 496 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$16$ |
$[16, 952, 30112, 925780, 28636336, 887509222, 27512631568, 852892028644, 26439631716832, 819628321295752]$ |
$573$ |
$[573, 915081, 897091092, 854979395001, 819834001771173, 787667699145519504, 756944415448828781397, 727423967136047191124649, 699053872660369611325954452, 671790556944586498299938663001]$ |
$6$ |
$6$ |
$2$ |
$2$ |
$1$ |
4.0.357264.1 |
$D_{4}$ |
simple |
| 2.31.aq_eu |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
|
✓ |
|
✓ |
✓ |
$1 - 16 x + 124 x^{2} - 496 x^{3} + 961 x^{4}$ |
$[0,\frac{1}{2},\frac{1}{2},1]$ |
$1$ |
$1$ |
$1$ |
$2$ |
$0$ |
$16$ |
$[16, 954, 30160, 926310, 28639536, 887514330, 27512526064, 852890779518, 26439624254224, 819628298555674]$ |
$574$ |
$[574, 917252, 898540174, 855469574288, 819925631796334, 787672232968187588, 756941512771733978206, 727422901767585032081408, 699053675351801188803600286, 671790538306173820886709585732]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.182528.1 |
$D_{4}$ |
simple |
| 2.31.aq_ev |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 9 x + 31 x^{2} )( 1 - 7 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$16$ |
$[16, 956, 30208, 926836, 28642576, 887516318, 27512382256, 852889221796, 26439615459328, 819628279571276]$ |
$575$ |
$[575, 919425, 899990000, 855956172825, 820012691114375, 787673998369440000, 756937556278180717175, 727421573201413405480425, 699053442818080395344390000, 671790522746023964873983160625]$ |
$7$ |
$7$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.31.aj $\times$ 1.31.ah |
| 2.31.aq_ew |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 8 x + 31 x^{2} )^{2}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$16$ |
$[16, 958, 30256, 927358, 28645456, 887515198, 27512200816, 852887374078, 26439605665936, 819628268587198]$ |
$576$ |
$[576, 921600, 901440576, 856439193600, 820095180388416, 787673006089113600, 756932564465162911296, 727419997301923617177600, 699053183884578456828196416, 671790513743165867950656000000]$ |
$14$ |
$14$ |
$6$ |
$6$ |
$1$ |
\(\Q(\sqrt{-15}) \) |
$C_2$ |
1.31.ai 2 |
| 2.31.ap_ec |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 11 x + 31 x^{2} )( 1 - 4 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$17$ |
$[17, 949, 29792, 921769, 28611227, 887433118, 27512640557, 852892263409, 26439622160672, 819628237137229]$ |
$588$ |
$[588, 910224, 887468400, 851274252864, 819115245162228, 787600160998560000, 756944662819622238948, 727424167364101867532544, 699053619999095057531343600, 671790487965881591797070941584]$ |
$6$ |
$6$ |
$24$ |
$12$ |
$6$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.31.al $\times$ 1.31.ae |
| 2.31.ap_ed |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 107 x^{2} - 465 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$17$ |
$[17, 951, 29837, 922243, 28614452, 887451531, 27512766767, 852893301043, 26439629657087, 819628278323406]$ |
$589$ |
$[589, 912361, 888819259, 851711802525, 819207542162704, 787616501866537561, 756948135214243669159, 727425052354676235597525, 699053818201491504304116409, 671790521723235652223090626816]$ |
$9$ |
$9$ |
$2$ |
$2$ |
$1$ |
4.0.16525.1 |
$D_{4}$ |
simple |
| 2.31.ap_ee |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 108 x^{2} - 465 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$17$ |
$[17, 953, 29882, 922713, 28617527, 887467178, 27512859377, 852894030673, 26439634767782, 819628301947073]$ |
$590$ |
$[590, 914500, 890170760, 852145732000, 819295548142250, 787630387848232000, 756950683172148524810, 727425674650901536272000, 699053953326358338861769640, 671790541085860878610509062500]$ |
$10$ |
$10$ |
$2$ |
$2$ |
$1$ |
4.0.67240.1 |
$D_{4}$ |
simple |
| 2.31.ap_ef |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 109 x^{2} - 465 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$17$ |
$[17, 955, 29927, 923179, 28620452, 887480071, 27512919017, 852894468739, 26439637777067, 819628311686350]$ |
$591$ |
$[591, 916641, 891522909, 852576043869, 819379263556176, 787641829635491721, 756952324028068787601, 727426048274280599309109, 699054032890736935906174299, 671790549068448093390331627776]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.1835829.1 |
$D_{4}$ |
simple |
| 2.31.ap_eg |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 110 x^{2} - 465 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$17$ |
$[17, 957, 29972, 923641, 28623227, 887490222, 27512946317, 852894631633, 26439638966012, 819628311110277]$ |
$592$ |
$[592, 918784, 892875712, 853002740736, 819458688872752, 787650837923221504, 756953075117147385712, 727426187205410695680000, 699054064326005664042046912, 671790548596283048399593755904]$ |
$16$ |
$16$ |
$2$ |
$2$ |
$1$ |
4.0.458469.1 |
$D_{4}$ |
simple |
| 2.31.ap_eh |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 111 x^{2} - 465 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$17$ |
$[17, 959, 30017, 924099, 28625852, 887497643, 27512941907, 852894535699, 26439638612447, 819628303679054]$ |
$593$ |
$[593, 920929, 894229175, 853425825229, 819533824573328, 787657423409460625, 756952953774961194683, 727426105383987577337589, 699054054977880349080742325, 671790542505443170361470845184]$ |
$7$ |
$7$ |
$2$ |
$2$ |
$1$ |
4.0.1706389.1 |
$D_{4}$ |
simple |
| 2.31.ap_ei |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 10 x + 31 x^{2} )( 1 - 5 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$17$ |
$[17, 961, 30062, 924553, 28628327, 887502346, 27512906417, 852894197233, 26439636990962, 819628292744281]$ |
$594$ |
$[594, 923076, 895583304, 853845300000, 819604671152454, 787661596795461696, 756951977337544587654, 727425816708809710800000, 699054012106414779242076264, 671790533542994312522729585316]$ |
$12$ |
$12$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-6}) \), \(\Q(\sqrt{-11}) \) |
$C_2$, $C_2$ |
1.31.ak $\times$ 1.31.af |
| 2.31.ap_ej |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 113 x^{2} - 465 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$17$ |
$[17, 963, 30107, 925003, 28630652, 887504343, 27512840477, 852893632483, 26439634372907, 819628281549198]$ |
$595$ |
$[595, 925225, 896938105, 854261167725, 819671229118000, 787663368785770225, 756950163141413540005, 727425335037782708968725, 699053942886001254069817495, 671790524367187512914116000000]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.1201725.4 |
$D_{4}$ |
simple |
| 2.31.ap_ek |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 114 x^{2} - 465 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$17$ |
$[17, 965, 30152, 925449, 28632827, 887503646, 27512744717, 852892857649, 26439631026392, 819628273228925]$ |
$596$ |
$[596, 927376, 898293584, 854673431104, 819733498991276, 787662750088304896, 756947528523590293436, 727424674187923965636864, 699053854405371178916406224, 671790517547655759718031160976]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.222241.1 |
$D_{4}$ |
simple |
| 2.31.ap_el |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 115 x^{2} - 465 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$17$ |
$[17, 967, 30197, 925891, 28634852, 887500267, 27512619767, 852891888883, 26439627216287, 819628270810702]$ |
$597$ |
$[597, 929529, 899649747, 855082092861, 819791481307152, 787659751414438569, 756944090821628584527, 727423847935367497183125, 699053753667595706892735057, 671790515565610764247002165504]$ |
$10$ |
$10$ |
$2$ |
$2$ |
$1$ |
4.0.64389.1 |
$D_{4}$ |
simple |
| 2.31.ap_em |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 9 x + 31 x^{2} )( 1 - 6 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$17$ |
$[17, 969, 30242, 926329, 28636727, 887494218, 27512466257, 852890742289, 26439623204222, 819628277214129]$ |
$598$ |
$[598, 931684, 901006600, 855487155744, 819845176614178, 787654383479080000, 756939867373639442818, 727422870015368995987584, 699053647590086430219471400, 671790520814039742056017217284]$ |
$4$ |
$4$ |
$4$ |
$2$ |
$1$ |
\(\Q(\sqrt{-43}) \), \(\Q(\sqrt{-22}) \) |
$C_2$, $C_2$ |
1.31.aj $\times$ 1.31.ag |
| 2.31.ap_en |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 15 x + 117 x^{2} - 465 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$17$ |
$[17, 971, 30287, 926763, 28638452, 887485511, 27512284817, 852889433923, 26439619248587, 819628295251406]$ |
$599$ |
$[599, 933841, 902364149, 855888622525, 819894585474704, 787646657000756281, 756934875518317563449, 727421754122311100145525, 699053543004596122957405619, 671790535597902202731763138816]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.103525.1 |
$D_{4}$ |
simple |
| 2.31.ap_eo |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
|
$( 1 - 8 x + 31 x^{2} )( 1 - 7 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$17$ |
$[17, 973, 30332, 927193, 28640027, 887474158, 27512076077, 852887979793, 26439615604532, 819628327627573]$ |
$600$ |
$[600, 936000, 903722400, 856286496000, 819939708465000, 787636582701696000, 756929132594968259400, 727420513909708884096000, 699053446657219537135677600, 671790562134326748922185000000]$ |
$0$ |
$0$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-15}) \), \(\Q(\sqrt{-3}) \) |
$C_2$, $C_2$ |
1.31.ai $\times$ 1.31.ah |
| 2.31.ao_dq |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 94 x^{2} - 434 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$18$ |
$[18, 954, 29694, 920670, 28608418, 887446650, 27512621070, 852890238078, 26439605489010, 819628186545274]$ |
$608$ |
$[608, 914432, 884560352, 850260819968, 819034854874848, 787612169443693568, 756944126607958814048, 727422439976924999057408, 699053179206722267381219168, 671790446499286675872192402432]$ |
$4$ |
$4$ |
$2$ |
$2$ |
$1$ |
4.0.2312.1 |
$D_{4}$ |
simple |
| 2.31.ao_dr |
$2$ |
$\F_{31}$ |
$31$ |
|
|
✓ |
✓ |
|
|
✓ |
✓ |
$( 1 - 11 x + 31 x^{2} )( 1 - 3 x + 31 x^{2} )$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$18$ |
$[18, 956, 29736, 921076, 28611078, 887464478, 27512774538, 852891514276, 26439613950456, 819628234038476]$ |
$609$ |
$[609, 916545, 885817296, 850635332505, 819110980551129, 787627992007584000, 756948348966745361769, 727423528435717388903145, 699053402924100045374703696, 671790485426055980232192128625]$ |
$8$ |
$8$ |
$12$ |
$6$ |
$1$ |
\(\Q(\sqrt{-3}) \), \(\Q(\sqrt{-115}) \) |
$C_2$, $C_2$ |
1.31.al $\times$ 1.31.ad |
| 2.31.ao_ds |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 96 x^{2} - 434 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$18$ |
$[18, 958, 29778, 921478, 28613598, 887479918, 27512900958, 852892548478, 26439620411778, 819628264765198]$ |
$610$ |
$[610, 918660, 887074810, 851006202960, 819183099006250, 787641695053242660, 756951827154337693810, 727424410498326975452160, 699053573758979468271395410, 671790510610544686469600662500]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.2376000.1 |
$D_{4}$ |
simple |
| 2.31.ao_dt |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 97 x^{2} - 434 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$18$ |
$[18, 960, 29820, 921876, 28615978, 887492982, 27513000918, 852893354916, 26439625101540, 819628281514480]$ |
$611$ |
$[611, 920777, 888332900, 851373433625, 819251210576331, 787653289252029200, 756954577348135235771, 727425098303008084747625, 699053697754501384020280100, 671790524338728910314166390137]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.3063872.2 |
$D_{4}$ |
simple |
| 2.31.ao_du |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
|
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 98 x^{2} - 434 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$1$ |
$1$ |
$18$ |
$[18, 962, 29862, 922270, 28618218, 887503682, 27513075006, 852893947774, 26439628245282, 819628286980802]$ |
$612$ |
$[612, 922896, 889591572, 851737026816, 819315315609012, 787662785277607824, 756956615725776496068, 727425603947087334641664, 699053780873852944825054212, 671790528819080649119268191376]$ |
$26$ |
$26$ |
$4$ |
$8$ |
$4$ |
\(\Q(i, \sqrt{13})\) |
$C_2^2$ |
simple |
| 2.31.ao_dv |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 99 x^{2} - 434 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$18$ |
$[18, 964, 29904, 922660, 28620318, 887512030, 27513123810, 852894341188, 26439630065520, 819628283764324]$ |
$613$ |
$[613, 925017, 890850832, 852096984873, 819375414463573, 787670193806016768, 756957958465156622773, 727425939486966124611273, 699053829000267809468345488, 671790526182764499252065462457]$ |
$12$ |
$12$ |
$2$ |
$2$ |
$1$ |
4.0.232848.1 |
$D_{4}$ |
simple |
| 2.31.ao_dw |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 100 x^{2} - 434 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$18$ |
$[18, 966, 29946, 923046, 28622278, 887518038, 27513147918, 852894549246, 26439630781746, 819628274371126]$ |
$614$ |
$[614, 927140, 892110686, 852453310160, 819431507511054, 787675525515738500, 756958621744445449334, 727426116938123274736640, 699053847937026372322053206, 671790518483834376488104258500]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.3755840.1 |
$D_{4}$ |
simple |
| 2.31.ao_dx |
$2$ |
$\F_{31}$ |
$31$ |
✓ |
✓ |
✓ |
✓ |
|
|
✓ |
✓ |
$1 - 14 x + 101 x^{2} - 434 x^{3} + 961 x^{4}$ |
$[0,0,1,1]$ |
$0$ |
$2$ |
$0$ |
$2$ |
$0$ |
$18$ |
$[18, 968, 29988, 923428, 28624098, 887521718, 27513147918, 852894585988, 26439630610428, 819628261213448]$ |
$615$ |
$[615, 929265, 893371140, 852806005065, 819483595134375, 787678791087770640, 756958621742106034215, 727426148275117817773065, 699053843407456020449529540, 671790507699430239713395040625]$ |
$8$ |
$8$ |
$2$ |
$2$ |
$1$ |
4.0.3624000.1 |
$D_{4}$ |
simple |
