-1
0
152
1031:[504, 2]
2053:[1008, 2]
4099:[4196]
8209:[8291]
16411:[8280, 2]
32771:[32545]
65537:[65115]
131101:[130579]
262147:[261873]
524309:[525362]
1048583:[1048721]
2097169:[2099343]
4194319:[4190448]
8388617:[4196176, 2]
16777259:[16776451]
33554467:[33556544]
67108879:[33553348, 2]
134217757:[134207016]
268435459:[268450764]
536870923:[536886729]
1073741827:[1073696739]
2147483659:[2147445985]
4294967311:[4294892145]
8589934609:[8589800815]
17179869209:[17179907771]
34359738421:[34359891299]
68719476767:[68719109932]
137438953481:[137439150447]
274877906951:[274876963417]
549755813911:[549755723143]
1099511627791:[1099510624080]
2199023255579:[1099512197774, 2]
4398046511119:[4398049864270]
8796093022237:[8796090641581]
17592186044423:[17592179180564]
35184372088891:[35184377696395]
70368744177679:[70368735914810]
140737488355333:[140737466844674]
281474976710677:[281474967245574]
562949953421381:[562949910045019]
1125899906842679:[562949923357406, 2]
2251799813685269:[2251799812875502]
4503599627370517:[4503599672855988]
9007199254740997:[9007199395723803]
18014398509482143:[18014398460825440]
36028797018963971:[18014398463069820, 2]
72057594037928017:[36028797145369816, 2]
144115188075855881:[144115187446866113]
288230376151711813:[288230375567209858]
576460752303423619:[576460752721346915]
1152921504606847009:[1152921506693313952]
2305843009213693967:[2305843010596733829]
4611686018427388039:[4611686021547019756]
9223372036854775837:[9223372041689460430]
15
1
1
163663
121661
1
1023
494
[4, [2, 2], [[-2147484185, 0], [0, 0]]]
2
2
0
0
0
1728
j
0
Mod(0, 5)
Mod(3, 5)
Mod(1, 2)*j
0
Mod(1, 3)*j
a
a
8*x^9 + 54*x^8 + 393*x^7 + 2373*x^6 + 6993*x^5 + 15267*x^4 + 19998*x^3 + 473
4*x^2 - 25880*x - 30932
16*x^33 + 20048*x^30 - 524864*x^27 - 20273280*x^24 - 35051520*x^21 - 1832755
20*x^18 - 818626560*x^15 - 1017937920*x^12 - 390856704*x^9 + 74973184*x^6 + 
102760448*x^3 + 4194304
[3.1096482423243803285501491221965830079, 1.55482412116219016427507456109829
15039 + 1.0643747452102737569438859937299427442*I]
[6.2192964846487606571002982443931660158, 3.10964824232438032855014912219658
30079 + 2.1287494904205475138877719874598854884*I]
[5.5614800275334595421263952543627169988, 2.78074001376672977106319762718135
84994 - 2.1374995527123861323185270948750077575*I]
[6.2192964846487606571002982443931660158, 3.10964824232438032855014912219658
30079 + 2.1287494904205475138877719874598854884*I]
[-1.1547274830668428355945002349018042438, -0.828886258466578582202749882549
09787812 + 0.52313677422798965199542236165917364573*I, -0.828886258466578582
20274988254909787812 - 0.52313677422798965199542236165917364573*I]
[10351, [1/2, -1, -2, 5/4], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]
]
[10351, [1, -1, 0, -1], 1, [11, 1; 941, 1], [[1, 5, 0, 1], [1, 5, 0, 1]]]
  ***   at top-level: E.omega
  ***                   ^-----
  *** _.omega: incorrect type in omega [not defined over C] (t_VEC).
[9, [9], [[Mod(3, 7), Mod(5, 7)]]]
[0, 0, 0, 413748, 716503104, 0, 827496, 2866012416, -171187407504, -19859904
, -619058681856, -226311754192704000000, 97158364170048/2807086984375, Vecsm
all([1]), [Vecsmall([128, -1])], [0, 0, 0, 0, 0, 0, 0, [[2, 3]~]]]
[1/30, -13/150, -1/10, -79/500]
1
[36, [36], [[a^2 + 1, a^3 + a^2 + a + 1]]]
1
[3, [3], [[0, 2]]]
1
[4, [4], [[Mod(3, 5), Mod(3, 5)]]]
[1 + 2*3 + 3^2 + 2*3^3 + 3^4 + 3^5 + 2*3^6 + 3^7 + O(3^8), 1 + 3 + 3^3 + 3^4
 + 2*3^5 + 2*3^6 + 2*3^7 + O(3^8), 3 + 2*3^3 + O(3^6), [1 + 2*3 + 3^2 + 2*3^
3 + 3^4 + 3^6 + 2*3^7 + O(3^8), 1 + 3 + 2*3^2 + 3^3 + 2*3^4 + 2*3^5 + 3^6 + 
3^7 + O(3^8)]]
[3^-1 + 2 + 2*3^2 + 2*3^5 + 2*3^6 + O(3^8)]~
[3^2 + 2*3^3 + 3^4 + 2*3^5 + 3^6 + 3^7 + 2*3^8 + 3^9 + O(3^10), 3 + 3^2 + 3^
4 + 3^5 + 2*3^6 + 2*3^7 + 2*3^8 + O(3^9), 3 + 2*3^3 + O(3^6), [3^-2 + 2*3^-1
 + 1 + 2*3 + 3^2 + 3^4 + 2*3^5 + O(3^6), 3^-2 + 3^-1 + 2 + 3 + 2*3^2 + 2*3^3
 + 3^4 + 3^5 + O(3^6)]]
error("incorrect type in obj_check (t_VEC).")
[2 + 2^6 + 2^10 + O(2^11), Mod(u, u^2 + (2 + 2^2 + 2^3 + 2^4 + 2^5 + 2^7 + 2
^8 + 2^9 + O(2^11))), 2^3 + 2^4 + O(2^8), [2^-3 + 2^2 + 2^4 + 2^7 + 2^10 + O
(2^11), 2^-3 + 2^2 + 2^5 + 2^6 + 2^10 + O(2^13)]]
x^-2 + 31/15*x^2 + 2501/756*x^4 + 961/675*x^6 + 77531/41580*x^8 + O(x^9)
[-1, -2*w]
[I, 1]
[[I, 1], [-3.1415926535897932384626433832795028842*I, 3.14159265358979323846
26433832795028842]]
[1, 1]
x^-2 - 1/5*x^2 - 1/7*x^4 + 1/75*x^6 + 3/385*x^8 + 277/238875*x^10 - 2/5775*x
^12 + O(x^14)
x^-2 - 1/5*x^2 - 1/7*x^4 + 1/75*x^6 + O(x^7)
8.9760336058655702799613054290253052728
-8.9795585687185301843619815765809019104
0.0070737179180847219897019688523688143761 - 4.54459013280902760664280136539
71181201*I
[1, 2]
x^-2 + 9.4536360064616926146530698267460656697*x^2 + 6.577345622 E-37*x^4 + 
29.790411247556326629130082765180921498*x^6 + 1.695813583 E-36*x^8 + 43.3273
39141107674122263886023453990048*x^10 + 3.562578744 E-36*x^12 + O(x^14)
x^-2 + 9.4536360064616926146530698267460656697*x^2 + 6.577345622 E-37*x^4 + 
29.790411247556326629130082765180921498*x^6 + O(x^7)
10.092015307351769584764433105625607145
-10.092015307351769584764433105625607145
3.2557987470773994635555990212606293690 E-38 - 2.704147351607435273075740713
3303875089*I
[1, 3]
x^-2 + 9.4536360064616926146530698267460656697*x^2 + 6.577345622 E-37*x^4 + 
29.790411247556326629130082765180921498*x^6 + 1.695813583 E-36*x^8 + 43.3273
39141107674122263886023453990048*x^10 + 3.562578744 E-36*x^12 + O(x^14)
x^-2 + 9.4536360064616926146530698267460656697*x^2 + 6.577345622 E-37*x^4 + 
29.790411247556326629130082765180921498*x^6 + O(x^7)
10.092015307351769584764433105625607145
-10.092015307351769584764433105625607145
3.2557987470773994635555990212606293690 E-38 - 2.704147351607435273075740713
3303875089*I
[2, 1]
x^-1 + 1/15*x^3 + 1/35*x^5 - 1/525*x^7 - 1/1155*x^9 - 277/2627625*x^11 + 2/7
5075*x^13 + O(x^15)
x^-1 + 1/15*x^3 + 1/35*x^5 - 1/525*x^7 + O(x^8)
3.0025857981852417376980007365038576528
-3.0023507303355942712341893343171384978*I
1.4945837634650773441141478432745008118 - 1.49552579635851441107083905597206
14467*I
[2, 2]
x^-1 - 3.1512120021538975382176899422486885566*x^3 - 1.315469124 E-37*x^5 - 
4.2557730353651895184471546807401316426*x^7 - 1.884237315 E-37*x^9 - 3.93884
90128279703747512623657685445499*x^11 - 2.740445188 E-37*x^13 + O(x^15)
x^-1 - 3.1512120021538975382176899422486885566*x^3 - 1.315469124 E-37*x^5 - 
4.2557730353651895184471546807401316426*x^7 + O(x^8)
2.8609969154308155967482927187353233603
-2.8813199850735158607638401394492232764*I
1.7185329556464940714815988649194112975 - 1.71853295564649407148159886491941
12976*I
[2, 3]
x^-1 - 3.1512120021538975382176899422486885566*x^3 - 1.315469124 E-37*x^5 - 
4.2557730353651895184471546807401316426*x^7 - 1.884237315 E-37*x^9 - 3.93884
90128279703747512623657685445499*x^11 - 2.740445188 E-37*x^13 + O(x^15)
x^-1 - 3.1512120021538975382176899422486885566*x^3 - 1.315469124 E-37*x^5 - 
4.2557730353651895184471546807401316426*x^7 + O(x^8)
2.8609969154308155967482927187353233603
-2.8813199850735158607638401394492232764*I
1.7185329556464940714815988649194112975 - 1.71853295564649407148159886491941
12976*I
[3, 1]
x + 1/60*x^5 + 1/210*x^7 - 1/10080*x^9 - 1/138600*x^11 - 167/259459200*x^13 
- 19/1513512000*x^15 + O(x^17)
x + 1/60*x^5 + 1/210*x^7 - 1/10080*x^9 + O(x^10)
0.33340409272605175654322174351877926789
0.33339973807064633526799756411632693200*I
0.33307632454406929865753194192439552171 + 0.3330414840427217068846417452694
8964209*I
[3, 2]
x - 0.78780300053847438455442248556217213914*x^5 - 2.192448541 E-38*x^7 - 0.
22165484559193695408578930628854852305*x^9 - 1.570197765 E-39*x^11 + 0.00936
19303173614540570518182056750707483*x^13 + 1.291380487 E-40*x^15 + O(x^17)
x - 0.78780300053847438455442248556217213914*x^5 - 2.192448541 E-38*x^7 - 0.
22165484559193695408578930628854852305*x^9 + O(x^10)
0.33008009031657824359527653587336069208
0.33008009031657824359527653587336069208*I
0.34612072856429482856153662202577445445 + 0.3461207285642948285615366220257
7445446*I
[3, 3]
x - 0.78780300053847438455442248556217213914*x^5 - 2.192448541 E-38*x^7 - 0.
22165484559193695408578930628854852305*x^9 - 1.570197765 E-39*x^11 + 0.00936
19303173614540570518182056750707483*x^13 + 1.291380487 E-40*x^15 + O(x^17)
x - 0.78780300053847438455442248556217213914*x^5 - 2.192448541 E-38*x^7 - 0.
22165484559193695408578930628854852305*x^9 + O(x^10)
0.33008009031657824359527653587336069208
0.33008009031657824359527653587336069208*I
0.34612072856429482856153662202577445445 + 0.3461207285642948285615366220257
7445446*I
[4, 1]
0
0
-1.0984000330177788282680372407424344829
-1.0984130942966868400436474225688716324 + 1.5707963267948966192313216916397
514421*I
-0.75286232322707031868584884787482252469 + 0.785345859584418994173505759767
90041015*I
[4, 2]
0
0
-1.1084199560389642415209208807828823872
-1.1084199560389642415209208807828823872 + 1.5707963267948966192313216916397
514421*I
-0.71439404801872849905771074604935970853 + 0.785398163397448309615660845819
87572105*I
[4, 3]
0
0
-1.1084199560389642415209208807828823872
-1.1084199560389642415209208807828823872 + 1.5707963267948966192313216916397
514421*I
-0.71439404801872849905771074604935970853 + 0.785398163397448309615660845819
87572105*I
[2.5135797437238231405782694715779164652, 1.25678987186191157028913473578895
82326 + 0.78959476569186174055147277865716603189*I]
[3.1415926535897932384626433832795028842, 9.42477796076937971538793014983850
86526*I]
(x)->elleisnum(x,2)
-2.9936282668967606065680548947245432597 - 7.1637767384648910133063235008836
078048*I
-37.699111843077518861551720599354034610
-37.699111843077518861551720599354034610
(x)->elleisnum(x,4,1)
-3.9999999999999999999999999999999999999 - 5.48564030 E-38*I
189.07272012923385229306139653492131339
189.07272012923385229306139653492131339
(x)->elleisnum(x,6,1)
-4.0000000000000000000000000000000000000 - 1.253860641 E-37*I
1.841656774 E-35
1.841656774 E-35
(x)->elleisnum(x,10)
-41471.999999999999999999999999999999998 - 7.70371978 E-34*I
-2.818118420 E-30
-2.818118420 E-30
-1
[0]
347813742467679407541/38941611811810745401
[1, [], []]
[2, [2], [[15, -8]]]
[3, [3], [[5, 9]]]
[4, [4], [[5, -2]]]
[5, [5], [[5, 5]]]
[6, [6], [[9, 23]]]
[7, [7], [[-1, 2]]]
[8, [8], [[2, 6]]]
[9, [9], [[-3, 7]]]
[10, [10], [[0, 9]]]
[12, [12], [[-9, 49]]]
[4, [2, 2], [[-29/4, 25/8], [-7, 3]]]
[8, [4, 2], [[-2, 3], [-1, 0]]]
[12, [6, 2], [[1, 2], [3, -2]]]
[16, [8, 2], [[4, 58], [-36, 18]]]
[16, [8, 2], [[117433600, 6734213027200], [352179456, -176089728]]]
[4, [2, 2], [[-1377493124511464657, 0], [-691668349248679055, 0]]]
[0.49999999999999999999999999999999999978 - 2.057115114 E-38*I, 1.9216402159
513147090074725264936203858 + 0.26019438802828824617801390769760176484*I]
3 + 11^2 + 2*11^3 + 3*11^4 + O(11^5)
Mod((2 + 3 + O(3^4))*u + (2*3 + 3^2 + O(3^4)), u^2 + (1 + 3 + 2*3^4 + 3^8 + 
2*3^9 + O(3^10)))
Mod((1 + 3 + 3^3 + 3^4 + 2*3^6 + 2*3^8 + 2*3^9 + O(3^10))*u + (1 + 3 + 3^2 +
 3^5 + 2*3^6 + 2*3^7 + 2*3^8 + 3^9 + O(3^10)), u^2 + (3 + 3^3 + 2*3^4 + 3^5 
+ 2*3^6 + 3^7 + 2*3^8 + 3^9 + 2*3^10 + 3^11 + 2*3^12 + O(3^13)))
Mod((2^3 + 2^7 + O(2^8))*u + (1 + 2 + 2^2 + 2^3 + 2^4 + O(2^6)), u^2 + (1 + 
2^2 + 2^4 + 2^5 + 2^7 + 2^8 + 2^9 + O(2^13)))
[Mod(0, 11), Mod(0, 11), Mod(0, 11), Mod(1, 11), Mod(1, 11), Mod(0, 11), Mod
(2, 11), Mod(4, 11), Mod(10, 11), Mod(7, 11), Mod(5, 11), Mod(10, 11), Mod(9
, 11), Vecsmall([3]), [11, [9, 5, [6, 0, 0, 0]]], [0, 0, 0, 0]]
1
[0.86602540378443864676372317075293618347 - 1/2*I, -0.8660254037844386467637
2317075293618348 - 1/2*I]
[-2, 3]
[0, 1]
[1, 0, 0, 0]
0.035247504442186170440172838583518049039
[0, 0, 0, 1, 1, 0, 2, 4, -1, -48, -864, -496, 6912/31, Vecsmall([1]), [Vecsm
all([128, -1])], [0, 0, 0, 0, 0, 0, 0, [[2, 3]~]]]
[0, 0, 0, 1/16, 1/64, 0, 1/8, 1/16, -1/256, -3, -27/2, -31/256, 6912/31, Vec
small([1]), [Vecsmall([128, -1])], [0, 0, 0, 0, 0, 0, 0, [[2, 3]~, [1/2, 0, 
0, 0], [0, 0, 0, 1, 1, 0, 2, 4, -1, -48, -864, -496, 6912/31, Vecsmall([1]),
 [Vecsmall([128, -1])], [0, 0, 0, 0, 0, 0, 0, [[2, 3]~]]]]]]

0
20 0 0 -16 0 -4 14 8 0 0 0 26 0 2 0 -28 
1728
0 0 -22 0 -14 0 -22 0 0 26 0 18 0 -14 2 0 
-3375
16 0 -10 0 -22 24 0 -20 0 0 4 0 8 -18 -26 0 
8000
0 -18 6 22 0 0 0 2 0 0 18 0 0 22 0 0 
54000
20 0 0 16 0 4 -14 -8 0 0 0 26 0 2 0 -28 
-32768
0 0 3 0 0 0 23 16 0 0 21 25 -15 0 0 -20 
287496
0 0 22 0 -14 0 22 0 0 -26 0 -18 0 14 2 0 
-884736
0 7 23 -9 11 0 18 -24 0 0 0 0 17 0 -22 -25 
-12288000
20 0 0 -23 0 19 14 25 0 0 0 7 0 23 0 -11 
16581375
16 0 10 0 22 24 0 -20 0 0 -4 0 8 -18 -26 0 
-884736000
11 0 0 -13 0 0 0 0 -25 -2 0 -6 0 -27 -10 0 
-147197952000
-21 -16 0 0 -23 1 5 7 20 -25 0 11 0 13 0 -27 
-262537412640768000
0 19 0 0 0 -21 0 0 4 -23 8 0 0 0 -25 -12 
4294985035
[0, 1, [5, 0, 0, 0], 1]
1
1
[6.2500000000000000000000000000000000000, -140.62500000000000000000000000000
000000]
[37247908142/10128208321, 7601802384416381/1019292757217119]
[0, 0, 0, x^2, x, 0, 2*x^2, 4*x, -x^4, -48*x^2, -864*x, -64*x^6 - 432*x^2, -
6912*x^4/(-4*x^4 - 27), Vecsmall([0]), [Vecsmall([128, 0])], [0, 0, 0, 0]]
  ***   at top-level: ellminimalmodel(E)
  ***                 ^------------------
  *** ellminimalmodel: incorrect type in checkell over Q (t_VEC).
  ***   at top-level: ellweilpairing(E,[0]
  ***                 ^--------------------
  *** ellweilpairing: incorrect type in checkell over Fq (t_VEC).
  ***   at top-level: ellinit([1])
  ***                 ^------------
  *** ellinit: incorrect type in ellxxx [not an elliptic curve (ell5)] (t_VEC).
  ***   at top-level: ellinit([1,1],quadge
  ***                 ^--------------------
  *** ellinit: incorrect type in elliptic curve base_ring (t_QUAD).
  ***   at top-level: ellinit([Mod(1,2),1]
  ***                 ^--------------------
  *** ellinit: incorrect type in elliptic curve base_ring (t_VEC).
  ***   at top-level: ellinit([O(2),1],ffg
  ***                 ^--------------------
  *** ellinit: incorrect type in elliptic curve base_ring (t_VEC).
  ***   at top-level: ellinit([O(2),1],1.)
  ***                 ^--------------------
  *** ellinit: incorrect type in elliptic curve base_ring (t_VEC).
[0, 0, 0, 1, 2, 0, 2, 8, -1, -48, -1728, -1792, 432/7, Vecsmall([0]), [Vecsm
all([128, -1])], [0, 0, 0, 0]]
[0, 0, 0, 0, 1, 0, 0, 4, 0, 0, 1, 3, 0, Vecsmall([4]), [0, [Vecsmall([0]), V
ecsmall([0, 1]), [Vecsmall([0, 1]), Vecsmall([0]), Vecsmall([0]), Vecsmall([
0])]]], [0, 0, 0, 0]]
  ***   at top-level: ellinit([ffgen(5),1]
  ***                 ^--------------------
  *** ellinit: inconsistent moduli in ellinit: 3 != 5
[0, 0, 0, 1.0000000000000000000000000000000000000, 1, 0, 2.00000000000000000
00000000000000000000, 4, -1.0000000000000000000000000000000000000, -48.00000
0000000000000000000000000000000, -864, -496.00000000000000000000000000000000
000, 222.96774193548387096774193548387096774, Vecsmall([0]), [Vecsmall([128,
 -1])], [0, 0, 0, 0]]
  ***   at top-level: ellinit([1.,Mod(1,3)
  ***                 ^--------------------
  *** ellinit: incorrect type in elliptic curve base_ring (t_VEC).
1
-1
1
1
x^-2 + Mod(-1/5*x, x^2 + 5)*x^2 + Mod(-1/15, x^2 + 5)*x^6 + Mod(2/975*x, x^2
 + 5)*x^10 + O(x^14)
x^-1 + Mod(1/15*x, x^2 + 5)*x^3 + Mod(1/105, x^2 + 5)*x^7 + Mod(-2/10725*x, 
x^2 + 5)*x^11 + O(x^15)
x + Mod(1/60*x, x^2 + 5)*x^5 + Mod(1/2016, x^2 + 5)*x^9 + Mod(23/51891840*x,
 x^2 + 5)*x^13 + O(x^17)
Mod(1, 1009)*x^-2 + Mod(807, 1009)*x^2 + Mod(148, 1009)*x^6 + Mod(368, 1009)
*x^10 + O(x^14)
Mod(1, 1009)*x^-1 + Mod(740, 1009)*x^3 + Mod(123, 1009)*x^7 + Mod(150, 1009)
*x^11 + O(x^15)
Mod(1, 1009)*x + Mod(185, 1009)*x^5 + Mod(101, 1009)*x^9 + Mod(990, 1009)*x^
13 + O(x^17)
-52760
-52832
Total time spent: 1048
