.pol: x
.a1: 0
.a2: 0
.a3: 0
.a4: 0
.a6: 0
NF
.codiff: [1, 553/1105; 0, 1/1105]
.diff: [1105, 553; 0, 1]
.disc: 1105
.index: 2
.nf: [y^2 - 1105, [2, 0], 1105, 2, [[1, -17.12077013859466140231529077105260
9448; 1, 16.120770138594661402315290771052609448], [1, -17.12077013859466140
2315290771052609448; 1, 16.120770138594661402315290771052609448], [16, -274;
 16, 258], [2, -1; -1, 553], [1105, 553; 0, 1], [553, 1; 1, 2], [1105, [553,
 276; 1, 552]], [5, 13, 17]], [-33.241540277189322804630581542105218897, 33.
241540277189322804630581542105218897], [2, y - 1], [1, 1; 0, 2], [1, 0, 0, 2
76; 0, 1, 1, -1]]
.p: [5, 13, 17]
.pol: y^2 - 1105
.r1: 2
.r2: 0
.roots: [-33.241540277189322804630581542105218897, 33.2415402771893228046305
81542105218897]
.sign: [2, 0]
.t2: [2, -1.0000000000000000000000000000000000000; -1.0000000000000000000000
000000000000000, 553.00000000000000000000000000000000000]
.zk: [1, 1/2*y - 1/2]
NF chvar
  *** nfinit: Warning: nonmonic polynomial. Result of the form [nf,c].
.codiff: [1/2, 0; 0, 1/4]
.diff: [4, 0; 0, 2]
.disc: -8
.index: 1
.nf: [y^2 + 2, [0, 1], -8, 1, [Mat([1, 0.E-57 + 1.41421356237309504880168872
42096980786*I]), [1, 1.4142135623730950488016887242096980786; 1, -1.41421356
23730950488016887242096980786], [16, 23; 16, -23], [2, 0; 0, -4], [4, 0; 0, 
2], [2, 0; 0, -1], [2, [0, -2; 1, 0]], [2]], [0.E-57 + 1.4142135623730950488
016887242096980786*I], [1, y], [1, 0; 0, 1], [1, 0, 0, -2; 0, 1, 1, 0]]
.p: [2]
.pol: y^2 + 2
.r1: 0
.r2: 1
.roots: [0.E-57 + 1.4142135623730950488016887242096980786*I]
.sign: [0, 1]
.t2: [2, 0.E-57; 0.E-57, 4.0000000000000000000000000000000000000]
.zk: [1, y]
BNF
.bnf: [[2, 0; 0, 2], [1, 1, 0; 1, 0, 1], [10.9503854058256053302677508250179
37393; -10.950385405825605330267750825017937393 + 3.141592653589793238462643
3832795028842*I], [-2.8070134016636593080928506577483570863, 6.4656286076812
397829259659980344686072, 1.8293076030087902374165576701430557605 + 3.141592
6535897932384626433832795028842*I, 0.E-38, 0.E-38; 2.80701340166365930809285
06577483570863 + 3.1415926535897932384626433832795028842*I, -6.4656286076812
397829259659980344686072 + 3.1415926535897932384626433832795028842*I, -1.829
3076030087902374165576701430557605 + 3.1415926535897932384626433832795028842
*I, 0.E-38, 0.E-38], [[2, [-1, 1]~, 1, 1, [0, 276; 1, -1]], [3, [-1, -1]~, 1
, 1, [0, -276; -1, 1]], [5, [1, 2]~, 2, 1, [1, 552; 2, -1]], [2, [2, 1]~, 1,
 1, [1, 276; 1, 0]], [3, [0, -1]~, 1, 1, [-1, -276; -1, 0]]], 0, [y^2 - 1105
, [2, 0], 1105, 2, [[1, -17.120770138594661402315290771052609448; 1, 16.1207
70138594661402315290771052609448], [1, -17.120770138594661402315290771052609
448; 1, 16.120770138594661402315290771052609448], [16, -274; 16, 258], [2, -
1; -1, 553], [1105, 553; 0, 1], [553, 1; 1, 2], [1105, [553, 276; 1, 552]], 
[5, 13, 17]], [-33.241540277189322804630581542105218897, 33.2415402771893228
04630581542105218897], [2, y - 1], [1, 1; 0, 2], [1, 0, 0, 276; 0, 1, 1, -1]
], [[4, [2, 2], [[2, 0; 0, 1], [3, 0; 0, 1]]], 10.95038540582560533026775082
5017937393, 1, [2, -1], [-857*y + 28488]], [[-1, 0; 0, -1], [0, 0; 0, 0], [2
.8070134016636593080928506577483570863, -6.465628607681239782925965998034468
6072; -2.8070134016636593080928506577483570863 - 3.1415926535897932384626433
832795028842*I, 6.4656286076812397829259659980344686072 - 3.1415926535897932
384626433832795028842*I], [Mat([1/2, 1]), Mat([1/3, 1])]~, [-1, 0; 0, -1], [
0, 0; 0, 0]], [0, 0, 0]]
.clgp: [4, [2, 2], [[2, 0; 0, 1], [3, 0; 0, 1]]]
.codiff: [1, 553/1105; 0, 1/1105]
.cyc: [2, 2]
.diff: [1105, 553; 0, 1]
.disc: 1105
.fu: [Mod(-857*y + 28488, y^2 - 1105)]
.gen: [[2, 0; 0, 1], [3, 0; 0, 1]]
.index: 2
.nf: [y^2 - 1105, [2, 0], 1105, 2, [[1, -17.12077013859466140231529077105260
9448; 1, 16.120770138594661402315290771052609448], [1, -17.12077013859466140
2315290771052609448; 1, 16.120770138594661402315290771052609448], [16, -274;
 16, 258], [2, -1; -1, 553], [1105, 553; 0, 1], [553, 1; 1, 2], [1105, [553,
 276; 1, 552]], [5, 13, 17]], [-33.241540277189322804630581542105218897, 33.
241540277189322804630581542105218897], [2, y - 1], [1, 1; 0, 2], [1, 0, 0, 2
76; 0, 1, 1, -1]]
.no: 4
.p: [5, 13, 17]
.pol: y^2 - 1105
.r1: 2
.r2: 0
.reg: 10.950385405825605330267750825017937393
.roots: [-33.241540277189322804630581542105218897, 33.2415402771893228046305
81542105218897]
.sign: [2, 0]
.t2: [2, -1.0000000000000000000000000000000000000; -1.0000000000000000000000
000000000000000, 553.00000000000000000000000000000000000]
.tu: [2, -1]
.zk: [1, 1/2*y - 1/2]
BNR
.bid: [[[4, 0; 0, 4], [0, 0]], [4, [2, 2], [[1, -2]~, [-1, -2]~]], [[[2, [-1
, 1]~, 1, 1, [0, 276; 1, -1]], 2; [2, [2, 1]~, 1, 1, [1, 276; 1, 0]], 2], [[
2, [-1, 1]~, 1, 1, [0, 276; 1, -1]], 2; [2, [2, 1]~, 1, 1, [1, 276; 1, 0]], 
2]], [[[[2], [[1, -2]~], [4, 1; 0, 1], [[[0, -1]~, [1, 1], [2, [-1, 1]~, 1, 
1, [0, 276; 1, -1]]]~, 1, [1, matrix(0,2)]], [1, 1, [[[2], [3], Mat([1, -1])
, 2]]], [[0]~, Mat(1)]], [[2], [[-1, -2]~], [4, 0; 0, 1], [[[1, -1]~, [1, 0]
, [2, [2, 1]~, 1, 1, [1, 276; 1, 0]]]~, 1, [1, matrix(0,2)]], [1, 1, [[[2], 
[3], Mat([1, 0]), 2]]], [[0]~, Mat(1)]]], [[], Vecsmall([])]], [[1; 0], [0; 
1]]]
.bnf: [[2, 0; 0, 2], [1, 1, 0; 1, 0, 1], [10.9503854058256053302677508250179
37393; -10.950385405825605330267750825017937393 + 3.141592653589793238462643
3832795028842*I], [-2.8070134016636593080928506577483570863, 6.4656286076812
397829259659980344686072, 1.8293076030087902374165576701430557605 + 3.141592
6535897932384626433832795028842*I, 0.E-38, 0.E-38; 2.80701340166365930809285
06577483570863 + 3.1415926535897932384626433832795028842*I, -6.4656286076812
397829259659980344686072 + 3.1415926535897932384626433832795028842*I, -1.829
3076030087902374165576701430557605 + 3.1415926535897932384626433832795028842
*I, 0.E-38, 0.E-38], [[2, [-1, 1]~, 1, 1, [0, 276; 1, -1]], [3, [-1, -1]~, 1
, 1, [0, -276; -1, 1]], [5, [1, 2]~, 2, 1, [1, 552; 2, -1]], [2, [2, 1]~, 1,
 1, [1, 276; 1, 0]], [3, [0, -1]~, 1, 1, [-1, -276; -1, 0]]], 0, [y^2 - 1105
, [2, 0], 1105, 2, [[1, -17.120770138594661402315290771052609448; 1, 16.1207
70138594661402315290771052609448], [1, -17.120770138594661402315290771052609
448; 1, 16.120770138594661402315290771052609448], [16, -274; 16, 258], [2, -
1; -1, 553], [1105, 553; 0, 1], [553, 1; 1, 2], [1105, [553, 276; 1, 552]], 
[5, 13, 17]], [-33.241540277189322804630581542105218897, 33.2415402771893228
04630581542105218897], [2, y - 1], [1, 1; 0, 2], [1, 0, 0, 276; 0, 1, 1, -1]
], [[4, [2, 2], [[2, 0; 0, 1], [3, 0; 0, 1]]], 10.95038540582560533026775082
5017937393, 1, [2, -1], [-857*y + 28488]], [[-1, 0; 0, -1], [0, 0; 0, 0], [2
.8070134016636593080928506577483570863, -6.465628607681239782925965998034468
6072; -2.8070134016636593080928506577483570863 - 3.1415926535897932384626433
832795028842*I, 6.4656286076812397829259659980344686072 - 3.1415926535897932
384626433832795028842*I], [Mat([1/2, 1]), Mat([1/3, 1])]~, [-1, 0; 0, -1], [
0, 0; 0, 0]], [0, [Mat([[16, -1]~, 1]), Mat([[129, -8]~, 1])], 0]]
.clgp: [4, [2, 2]]
.codiff: [1, 553/1105; 0, 1/1105]
.cyc: [2, 2]
.diff: [1105, 553; 0, 1]
.disc: 1105
.index: 2
.mod: [[4, 0; 0, 4], [0, 0]]
.nf: [y^2 - 1105, [2, 0], 1105, 2, [[1, -17.12077013859466140231529077105260
9448; 1, 16.120770138594661402315290771052609448], [1, -17.12077013859466140
2315290771052609448; 1, 16.120770138594661402315290771052609448], [16, -274;
 16, 258], [2, -1; -1, 553], [1105, 553; 0, 1], [553, 1; 1, 2], [1105, [553,
 276; 1, 552]], [5, 13, 17]], [-33.241540277189322804630581542105218897, 33.
241540277189322804630581542105218897], [2, y - 1], [1, 1; 0, 2], [1, 0, 0, 2
76; 0, 1, 1, -1]]
.no: 4
.p: [5, 13, 17]
.pol: y^2 - 1105
.r1: 2
.r2: 0
.roots: [-33.241540277189322804630581542105218897, 33.2415402771893228046305
81542105218897]
.sign: [2, 0]
.t2: [2, -1.0000000000000000000000000000000000000; -1.0000000000000000000000
000000000000000, 553.00000000000000000000000000000000000]
.zk: [1, 1/2*y - 1/2]
.zkst: [4, [2, 2], [[1, -2]~, [-1, -2]~]]
RNF
.disc: [[4420, 553; 0, 1], [1, 2]~]
.index: [2, 0; 0, 1]
.nf: [y^2 - 1105, [2, 0], 1105, 2, [[1, -17.12077013859466140231529077105260
9448; 1, 16.120770138594661402315290771052609448], [1, -17.12077013859466140
2315290771052609448; 1, 16.120770138594661402315290771052609448], [16, -274;
 16, 258], [2, -1; -1, 553], [1105, 553; 0, 1], [553, 1; 1, 2], [1105, [553,
 276; 1, 552]], [5, 13, 17]], [-33.241540277189322804630581542105218897, 33.
241540277189322804630581542105218897], [2, y - 1], [1, 1; 0, 2], [1, 0, 0, 2
76; 0, 1, 1, -1]]
.pol: x^2 - y
.polabs: x^4 - 1105
.zk: [[1, x - 1], [1, [1, 1/2; 0, 1/2]]]
QUADCLASSUNIT
.clgp: [4, [2, 2], [Qfb(2, 33, -2, 0.E-38), Qfb(3, 31, -12, 0.E-38)]]
.cyc: [2, 2]
.gen: [Qfb(2, 33, -2, 0.E-38), Qfb(3, 31, -12, 0.E-38)]
.no: 4
.reg: 10.950385405825605330267750825017937393
GAL
.gen: [Vecsmall([2, 1])]
.group: [Vecsmall([1, 2]), Vecsmall([2, 1])]
.mod: 1924481769277537925474295096745532701170466590649506396700122170162248
74137973943
.orders: Vecsmall([2])
.p: 7
.pol: x^2 - 680564733841876926926749214863536422912
.roots: [8115106970904773215875220506543554430286346080245400415743406046580
3070437569694, 1112971072187060603886773046091177258141831982624966355125781
56550421803700404249]~
ELL
.a1: 1
.a2: 2
.a3: 3
.a4: 4
.a6: 5
.b2: 9
.b4: 11
.b6: 29
.b8: 35
.c4: -183
.c6: -3429
.area: 2.9719152678179096707716479509361896060
.disc: -10351
.eta: [3.1096482423243803285501491221965830079, 1.55482412116219016427507456
10982915039 + 1.0643747452102737569438859937299427442*I]
.gen: [[1, 2]]
.j: 6128487/10351
.omega: [2.7807400137667297710631976271813584994, 1.390370006883364885531598
8135906792497 - 1.0687497763561930661592635474375038788*I]
.roots: [-1.6189099322673713423780009396072169751, -0.3155450338663143288109
9953019639151248 + 2.0925470969119586079816894466366945829*I, -0.31554503386
631432881099953019639151248 - 2.0925470969119586079816894466366945829*I, 4.1
850941938239172159633788932733891659*I, -1.303364898401057013567001409410825
4626 + 2.0925470969119586079816894466366945829*I, -1.30336489840105701356700
14094108254626 - 2.0925470969119586079816894466366945829*I]~
ELLFp
.a1: Mod(1, 13)
.a2: Mod(2, 13)
.a3: Mod(3, 13)
.a4: Mod(4, 13)
.a6: Mod(5, 13)
.b2: Mod(9, 13)
.b4: Mod(11, 13)
.b6: Mod(3, 13)
.b8: Mod(9, 13)
.c4: Mod(12, 13)
.c6: Mod(3, 13)
.cyc: [13]
.disc: Mod(10, 13)
.gen: [[Mod(6, 13), Mod(12, 13)]]
.group: [13, [13], [[Mod(6, 13), Mod(12, 13)]]]
.j: Mod(9, 13)
.no: 13
.p: 13
ELLFq
.a1: 1
.a2: 2
.a3: 3
.a4: 4
.a6: 5
.b2: 9
.b4: 11
.b6: 3
.b8: 9
.c4: 12
.c6: 3
.cyc: [195]
.disc: 10
.gen: [[6*x + 1, x + 6]]
.group: [195, [195], [[6*x + 1, x + 6]]]
.j: 9
.no: 195
.p: 13
ELLQp
.a1: 1
.a2: 2
.a3: 3
.a4: 4
.a6: 5
.b2: 9
.b4: 11
.b6: 29
.b8: 35
.c4: -183
.c6: -3429
.disc: -10351
.group: [12, [12], [[10, 4]]]
.j: 6128487/10351
.p: 11
.roots: [9 + O(11^2)]~
.tate: [6 + 8*11 + 5*11^2 + 8*11^4 + O(11^5), Mod(x, x^2 + (5 + 2*11 + 5*11^
2 + 10*11^3 + 2*11^4 + O(11^5))), 3*11 + 7*11^2 + O(11^5), [6 + 3*11 + O(11^
5), 6 + 11 + 9*11^2 + 11^3 + 2*11^4 + O(11^5)], 1, [[39, 134943, 48065, 1359
11], [31719, 92956, 62706, 135911], [2*11 + 2*11^2 + 9*11^3 + 8*11^4 + O(11^
5), 6*11^2 + 9*11^3 + 2*11^4 + O(11^5), 10*11^4 + O(11^5)], 0]]
FFELT
.f: 3
.mod: x^3 + x^2 + 1
.p: 2
.pol: x
.f: 3
.mod: x^3 + 2*x + 2
.p: 3
.pol: x
.f: 2
.mod: x^2 + x + 1
.p: 18446744073709551629
.pol: x
INTMOD
.mod: 3
POLMOD
.mod: x^2 + 1
.pol: x
QFB
QUAD
.disc: -4
.fu: []
.mod: w^2 + 1
.pol: w^2 + 1
.tu: [4, w]
.zk: [1, w]
PRID
.e: 1
.f: 1
.gen: [2, [-1, 1]~]
.p: 2
PADIC
.mod: 9
.p: 3
MODPR
.e: 1
.f: 1
.gen: [2, [-1, 1]~]
.p: 2
BID
.bid: [[[4, 1; 0, 1], [0, 0]], [2, [2], [3]], [Mat([[2, [-1, 1]~, 1, 1, [0, 
276; 1, -1]], 2]), Mat([[2, [-1, 1]~, 1, 1, [0, 276; 1, -1]], 2])], [[[[2], 
[3], [4, 1; 0, 1], [[[0, -1]~, [1, 1], [2, [-1, 1]~, 1, 1, [0, 276; 1, -1]]]
~, 1, [1, matrix(0,2)]], [1, 1, [[[2], [3], Mat([1, -1]), 2]]], [[0]~, Mat(1
)]]], [[], Vecsmall([])]], [Mat(1)]]
.clgp: [2, [2], [3]]
.cyc: [2]
.gen: [3]
.mod: [[4, 1; 0, 1], [0, 0]]
.no: 2
.zkst: [2, [2], [3]]
BID (nogen)
.bid: [[[4, 1; 0, 1], [0, 0]], [2, [2]], [Mat([[2, [-1, 1]~, 1, 1, [0, 276; 
1, -1]], 2]), Mat([[2, [-1, 1]~, 1, 1, [0, 276; 1, -1]], 2])], [[[[2], [3], 
[4, 1; 0, 1], [[[0, -1]~, [1, 1], [2, [-1, 1]~, 1, 1, [0, 276; 1, -1]]]~, 1,
 [1, matrix(0,2)]], [1, 1, [[[2], [3], Mat([1, -1]), 2]]], [[0]~, Mat(1)]]],
 [[], Vecsmall([])]], [Mat(1)]]
.clgp: [2, [2]]
.cyc: [2]
.mod: [[4, 1; 0, 1], [0, 0]]
.no: 2
.zkst: [2, [2]]

[1/3   0   0]

[  0 1/6   0]

[  0   0 1/6]

MF
.mod: t^2 + t + 1
.mod: Mod(1, t^2 + t + 1)*y^2 + Mod(-2*t, t^2 + t + 1)
Total time spent: 59
