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av_fq_isog • Show schema
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{'abvar_count': 2016, 'abvar_counts': [2016, 5225472, 10844832096, 23794876514304, 52593792166663776, 116191681342537522176, 256666965375589620673248, 566977346036181193339699200, 1252453076060539661923910256864, 2766668731694491744538914517425152], 'abvar_counts_str': '2016 5225472 10844832096 23794876514304 52593792166663776 116191681342537522176 256666965375589620673248 566977346036181193339699200 1252453076060539661923910256864 2766668731694491744538914517425152 ', 'angle_corank': 1, 'angle_rank': 1, 'angles': [0.35583038084852, 0.5], 'center_dim': 4, 'cohen_macaulay_max': 2, 'curve_count': 42, 'curve_counts': [42, 2362, 104454, 4876318, 229321722, 10779233722, 506623079382, 23811285550846, 1119130526924298, 52599132610972282], 'curve_counts_str': '42 2362 104454 4876318 229321722 10779233722 506623079382 23811285550846 1119130526924298 52599132610972282 ', 'curves': ['y^2=37*x^6+44*x^5+3*x^4+32*x^3+44*x^2+13*x+22', 'y^2=3*x^5+32*x^4+44*x^3+15*x^2+33*x+34', 'y^2=32*x^6+12*x^5+42*x^4+39*x^3+10*x^2+3*x+7', 'y^2=4*x^6+13*x^5+3*x^4+6*x^3+43*x^2+11*x+15', 'y^2=13*x^6+4*x^5+10*x^4+46*x^3+42*x^2+38*x+26', 'y^2=15*x^6+42*x^5+29*x^4+44*x^3+35*x^2+3*x+41', 'y^2=8*x^6+41*x^5+40*x^4+17*x^3+40*x^2+41*x+8', 'y^2=25*x^6+11*x^5+24*x^4+45*x^3+21*x^2+16*x+34', 'y^2=29*x^6+4*x^5+13*x^4+4*x^3+9*x^2+4*x+41', 'y^2=44*x^6+22*x^5+30*x^4+16*x^3+5*x^2+45*x+15', 'y^2=43*x^6+35*x^5+18*x^4+34*x^3+18*x^2+35*x+43', 'y^2=39*x^6+8*x^5+44*x^4+17*x^3+13*x^2+43*x+33', 'y^2=39*x^6+11*x^5+5*x^4+8*x^3+35*x^2+22*x+29', 'y^2=36*x^6+46*x^5+19*x^4+45*x^3+19*x^2+46*x+36', 'y^2=45*x^6+14*x^5+16*x^4+8*x^3+3*x^2+8*x+39', 'y^2=9*x^6+4*x^5+15*x^4+44*x^3+23*x^2+14*x+6', 'y^2=11*x^6+28*x^5+36*x^4+28*x^3+36*x^2+28*x+11', 'y^2=11*x^6+13*x^5+22*x^4+24*x^3+39*x^2+36*x+8', 'y^2=9*x^6+28*x^5+30*x^4+6*x^3+22*x^2+9*x+32', 'y^2=x^6+42*x^5+35*x^4+12*x^3+35*x^2+42*x+1', 'y^2=31*x^6+7*x^5+12*x^4+9*x^3+25*x^2+17*x+22', 'y^2=45*x^6+33*x^5+8*x^4+5*x^3+8*x^2+33*x+45', 'y^2=9*x^6+15*x^5+17*x^4+45*x^3+46*x^2+46*x+41', 'y^2=15*x^6+4*x^5+2*x^4+32*x^3+32*x^2+11*x+20', 'y^2=23*x^6+10*x^5+41*x^4+34*x^3+34*x^2+16*x+12', 'y^2=13*x^6+39*x^5+19*x^4+5*x^3+37*x^2+39*x+11', 'y^2=34*x^6+33*x^5+40*x^4+46*x^3+43*x^2+45*x+29', 'y^2=29*x^6+34*x^5+16*x^4+26*x^3+39*x^2+33*x+11', 'y^2=35*x^6+45*x^5+12*x^4+38*x^3+36*x^2+29*x+27', 'y^2=45*x^6+x^5+14*x^4+44*x^3+44*x^2+x+44', 'y^2=3*x^6+26*x^5+37*x^4+x^3+33*x^2+36*x+31', 'y^2=30*x^6+4*x^5+10*x^4+5*x^3+8*x^2+x+34', 'y^2=39*x^6+16*x^5+17*x^4+37*x^3+19*x^2+26*x+10', 'y^2=41*x^6+10*x^5+16*x^4+11*x^3+6*x^2+44*x+23', 'y^2=20*x^6+32*x^5+3*x^4+44*x^3+3*x^2+32*x+20', 'y^2=44*x^6+36*x^5+42*x^4+22*x^3+29*x^2+35*x+2', 'y^2=40*x^5+41*x^4+7*x^3+5*x^2+33*x', 'y^2=38*x^6+45*x^5+23*x^4+14*x^3+23*x^2+45*x+38', 'y^2=25*x^5+9*x^4+23*x^3+4*x^2+31*x+7', 'y^2=43*x^6+44*x^5+4*x^4+29*x^3+10*x^2+14*x+16', 'y^2=40*x^6+7*x^5+11*x^4+30*x^3+5*x^2+7*x+1', 'y^2=45*x^6+19*x^5+35*x^4+9*x^3+25*x^2+14*x+21', 'y^2=33*x^6+15*x^5+40*x^4+10*x^3+37*x^2+8*x+22', 'y^2=9*x^6+9*x^5+37*x^4+39*x^3+41*x^2+29*x+17', 'y^2=10*x^6+7*x^5+30*x^4+39*x^3+36*x^2+20*x+37', 'y^2=30*x^6+10*x^5+17*x^4+34*x^3+41*x^2+41*x+18', 'y^2=34*x^6+10*x^5+32*x^4+33*x^3+28*x^2+44*x+46', 'y^2=34*x^6+5*x^5+28*x^4+15*x^3+11*x^2+14*x', 'y^2=20*x^6+24*x^5+43*x^4+13*x^3+11*x^2+36*x+14', 'y^2=2*x^6+2*x^5+46*x^4+8*x^3+13*x^2+25*x', 'y^2=46*x^6+45*x^5+x^4+12*x^3+12*x^2+18*x+19', 'y^2=30*x^6+29*x^5+38*x^4+33*x^3+17*x^2+12*x+23', 'y^2=35*x^6+5*x^5+34*x^4+32*x^3+38*x+16', 'y^2=15*x^6+11*x^4+32*x^3+43*x^2+30', 'y^2=36*x^6+9*x^5+32*x^4+7*x^3+32*x^2+9*x+36', 'y^2=4*x^6+19*x^5+27*x^4+14*x^3+29*x^2+44*x+3', 'y^2=34*x^6+17*x^5+22*x^4+33*x^3+31*x^2+14*x', 'y^2=26*x^6+19*x^5+37*x^4+31*x^3+46*x^2+44*x+32', 'y^2=26*x^6+43*x^5+22*x^4+3*x^3+5*x^2+4*x+43', 'y^2=11*x^6+34*x^5+24*x^4+22*x^3+18*x^2+25*x+23', 'y^2=16*x^6+40*x^5+20*x^4+12*x^3+20*x^2+40*x+16', 'y^2=26*x^6+2*x^5+20*x^4+33*x^3+23*x^2+45*x+15', 'y^2=31*x^6+33*x^5+32*x^4+11*x^3+10*x^2+29*x+42', 'y^2=31*x^6+36*x^5+12*x^4+4*x^3+34*x^2+3*x+21', 'y^2=5*x^6+22*x^5+9*x^4+6*x^3+18*x^2+41*x+40', 'y^2=17*x^6+16*x^5+8*x^4+36*x^3+8*x^2+16*x+17', 'y^2=21*x^6+37*x^5+29*x^4+13*x^3+3*x^2+10*x+2', 'y^2=25*x^6+30*x^5+32*x^4+3*x^3+32*x^2+30*x+25', 'y^2=9*x^6+2*x^5+19*x^4+28*x^3+19*x^2+2*x+9', 'y^2=27*x^6+3*x^5+34*x^4+14*x^3+17*x^2+35', 'y^2=24*x^6+30*x^5+5*x^4+45*x^3+40*x^2+40*x+21', 'y^2=38*x^6+9*x^5+24*x^4+2*x^3+24*x^2+9*x+38', 'y^2=43*x^6+40*x^5+46*x^4+23*x^3+22*x^2+39*x+18', 'y^2=37*x^6+28*x^5+45*x^4+34*x^3+36*x^2+3*x+37', 'y^2=31*x^6+15*x^5+20*x^4+15*x^2+29*x+5', 'y^2=17*x^6+22*x^5+4*x^4+16*x^3+4*x^2+22*x+17', 'y^2=46*x^6+35*x^5+6*x^4+31*x^3+21*x+15', 'y^2=12*x^6+24*x^5+12*x^4+17*x^3+30*x^2+2*x+36', 'y^2=27*x^5+12*x^4+41*x^3+11*x^2+2*x+36', 'y^2=44*x^6+19*x^5+32*x^4+25*x^3+36*x^2+20*x+20', 'y^2=23*x^6+5*x^5+43*x^4+4*x^3+27*x^2+36*x+30', 'y^2=10*x^6+x^5+44*x^4+17*x^3+12*x^2+5*x+21', 'y^2=15*x^5+x^4+22*x^3+25*x^2+35*x+22', 'y^2=19*x^6+28*x^5+10*x^4+34*x^3+42*x^2+27*x+13', 'y^2=19*x^6+45*x^5+17*x^4+23*x^3+25*x^2+44*x+41', 'y^2=45*x^6+25*x^5+15*x^4+14*x^3+30*x^2+6*x+31', 'y^2=23*x^6+10*x^5+36*x^4+14*x^3+36*x^2+10*x+23', 'y^2=24*x^6+35*x^5+3*x^4+36*x^3+5*x^2+28*x+27', 'y^2=30*x^6+16*x^5+20*x^4+16*x^3+28*x^2+37*x+40', 'y^2=x^6+33*x^5+2*x^4+18*x^3+24*x^2+42*x+30', 'y^2=19*x^6+26*x^5+11*x^4+40*x^3+43*x^2+17*x+3', 'y^2=23*x^6+45*x^5+10*x^4+29*x^3+42*x^2+8*x+32', 'y^2=40*x^6+38*x^5+33*x^4+32*x^3+17*x^2+20*x+26', 'y^2=40*x^6+31*x^5+44*x^4+13*x^3+39*x^2+21*x+5', 'y^2=39*x^6+7*x^5+10*x^4+25*x^3+2*x+40', 'y^2=42*x^6+32*x^5+12*x^4+11*x^3+24*x^2+34*x+7', 'y^2=45*x^6+15*x^5+33*x^4+10*x^3+33*x^2+15*x+45', 'y^2=16*x^6+11*x^5+5*x^4+42*x^3+46*x^2+40*x+27', 'y^2=23*x^5+12*x^4+32*x^3+5*x^2+27*x+45', 'y^2=45*x^6+2*x^5+36*x^4+29*x^3+6*x^2+34*x+10', 'y^2=31*x^6+38*x^5+16*x^4+22*x^3+16*x^2+38*x+31', 'y^2=33*x^6+19*x^5+10*x^4+43*x^3+18*x^2+38*x+43', 'y^2=15*x^6+18*x^5+19*x^4+3*x^3+2*x^2+7*x+44', 'y^2=12*x^5+5*x^4+25*x^3+22*x^2+22*x+13', 'y^2=29*x^6+23*x^5+17*x^4+21*x^3+28*x^2+38*x+11', 'y^2=29*x^6+45*x^5+22*x^4+13*x^3+22*x^2+45*x+29', 'y^2=9*x^6+32*x^5+15*x^4+23*x^3+41*x^2+7*x+29', 'y^2=18*x^6+3*x^5+23*x^4+10*x^3+42*x^2+37*x+27', 'y^2=12*x^6+27*x^5+16*x^4+31*x^3+29*x^2+22*x+39', 'y^2=31*x^6+39*x^5+3*x^4+13*x^2+2*x+6', 'y^2=7*x^6+11*x^5+31*x^4+40*x^3+25*x^2+37*x+33', 'y^2=46*x^6+43*x^5+9*x^4+17*x^3+45*x^2+43*x+7', 'y^2=21*x^6+29*x^5+7*x^4+41*x^3+33*x^2+33*x+24', 'y^2=13*x^6+31*x^5+31*x^4+5*x^3+12*x^2+46*x+26', 'y^2=27*x^6+16*x^5+31*x^4+31*x^3+5*x^2+28*x+8', 'y^2=40*x^6+38*x^5+25*x^4+27*x^3+25*x^2+38*x+40', 'y^2=21*x^5+33*x^4+2*x^3+3*x^2+32*x+6', 'y^2=28*x^6+7*x^5+9*x^4+28*x^3+16*x^2+14*x+16', 'y^2=30*x^6+19*x^5+32*x^4+40*x^3+32*x^2+19*x+30', 'y^2=34*x^6+39*x^5+35*x^4+35*x^3+13*x^2+29*x+43', 'y^2=11*x^6+2*x^5+26*x^4+4*x^3+34*x^2+22*x+4', 'y^2=45*x^6+46*x^5+13*x^4+23*x+19', 'y^2=40*x^6+24*x^5+37*x^4+27*x^3+7*x^2+34*x+46', 'y^2=30*x^6+35*x^5+14*x^4+20*x^3+24*x^2+29*x+10', 'y^2=x^6+14*x^5+12*x^4+5*x^3+12*x^2+14*x+1', 'y^2=9*x^6+32*x^5+44*x^4+14*x^3+33*x^2+18*x+6', 'y^2=3*x^6+39*x^5+12*x^4+35*x^3+12*x^2+39*x+3', 'y^2=42*x^6+32*x^5+34*x^4+31*x^3+6*x^2+31*x', 'y^2=26*x^6+46*x^5+16*x^4+x^3+33*x+16', 'y^2=26*x^6+12*x^5+36*x^4+16*x^3+27*x^2+22*x+17', 'y^2=3*x^6+33*x^5+29*x^4+40*x^3+44*x^2+25*x+2', 'y^2=46*x^6+16*x^5+26*x^4+18*x^3+22*x^2+46*x', 'y^2=45*x^5+23*x^4+9*x^3+41*x^2+41*x', 'y^2=2*x^6+11*x^5+10*x^4+46*x^3+10*x^2+11*x+2', 'y^2=12*x^6+19*x^5+35*x^4+18*x^3+32*x^2+43*x+37', 'y^2=22*x^6+41*x^5+39*x^4+26*x^3+30*x^2+39*x+31', 'y^2=15*x^6+5*x^5+30*x^4+3*x^3+30*x^2+5*x+15', 'y^2=42*x^6+30*x^5+33*x^4+14*x^3+14*x^2+21*x+8', 'y^2=6*x^6+33*x^5+38*x^4+13*x^3+33*x^2+29*x+40', 'y^2=11*x^6+35*x^5+37*x^4+31*x^3+2*x^2+39*x+33', 'y^2=25*x^6+29*x^5+28*x^4+2*x^3+28*x^2+29*x+25', 'y^2=4*x^6+14*x^5+44*x^4+7*x^3+31*x^2+17*x+8', 'y^2=32*x^6+28*x^5+40*x^4+29*x^3+40*x^2+28*x+32', 'y^2=32*x^6+42*x^5+16*x^4+5*x^3+24*x^2+31*x+13', 'y^2=20*x^6+35*x^5+13*x^4+34*x^3+9*x^2+32*x+10', 'y^2=7*x^6+4*x^5+35*x^4+4*x^3+20*x^2+14*x+30', 'y^2=10*x^6+32*x^5+2*x^4+11*x^2+11*x+43', 'y^2=30*x^6+32*x^5+5*x^4+30*x^3+23*x^2+21*x+23', 'y^2=41*x^6+46*x^5+22*x^3+46*x+41', 'y^2=33*x^6+5*x^5+6*x^4+23*x^3+3*x^2+14*x+12', 'y^2=30*x^6+19*x^5+21*x^4+38*x^3+37*x^2+3*x+41', 'y^2=44*x^6+46*x^5+23*x^4+32*x^3+33*x^2+35*x+14', 'y^2=24*x^6+17*x^5+25*x^4+24*x^3+41*x^2+32*x', 'y^2=4*x^6+23*x^5+27*x^4+37*x^3+44*x^2+19*x+4', 'y^2=30*x^6+36*x^5+5*x^4+27*x^3+30*x^2+29*x+2', 'y^2=7*x^6+39*x^5+35*x^4+10*x^3+19*x^2+x+19', 'y^2=30*x^6+32*x^5+20*x^4+27*x^3+18*x^2+33*x+31', 'y^2=22*x^6+44*x^5+17*x^4+33*x^3+2*x^2+7*x+26', 'y^2=4*x^6+18*x^5+20*x^4+46*x^3+40*x^2+30*x+15', 'y^2=29*x^6+45*x^5+14*x^4+4*x^3+28*x^2+37*x+45', 'y^2=23*x^6+23*x^5+38*x^4+13*x^3+11*x^2+30*x+44', 'y^2=26*x^5+46*x^4+x^3+11*x^2+27*x+24', 'y^2=13*x^6+16*x^5+4*x^4+41*x^3+x^2+3*x+28', 'y^2=35*x^6+22*x^5+34*x^4+31*x^3+8*x^2+22*x+13', 'y^2=4*x^6+34*x^5+45*x^4+28*x^3+41*x^2+2*x+8', 'y^2=44*x^6+10*x^5+22*x^4+44*x^3+14*x^2+17*x+43', 'y^2=2*x^6+2*x^4+39*x^3+22*x^2+8*x+3', 'y^2=21*x^6+10*x^5+25*x^4+17*x^3+38*x^2+2*x+2', 'y^2=x^6+43*x^5+28*x^4+7*x^3+34*x^2+x+46', 'y^2=20*x^6+25*x^5+25*x^4+18*x^3+7*x^2+17*x+29', 'y^2=43*x^6+18*x^5+25*x^4+4*x^3+25*x^2+18*x+43', 'y^2=15*x^6+17*x^5+32*x^4+18*x^3+37*x^2+46*x+7', 'y^2=35*x^6+36*x^5+41*x^4+33*x^3+22*x^2+6*x+3', 'y^2=15*x^6+29*x^5+9*x^4+4*x^3+12*x^2+15*x+46', 'y^2=34*x^6+19*x^5+18*x^4+30*x^3+18*x^2+19*x+34', 'y^2=39*x^6+29*x^5+22*x^4+43*x^3+45*x^2+15*x+35', 'y^2=46*x^6+27*x^5+8*x^4+16*x^3+8*x^2+27*x+46', 'y^2=x^6+9*x^5+14*x^4+30*x^3+16*x^2+17*x+46', 'y^2=39*x^6+46*x^5+19*x^4+24*x^3+12*x^2+33*x+32', 'y^2=4*x^6+26*x^5+38*x^4+21*x^3+32*x^2+38*x+11'], 'dim1_distinct': 2, 'dim1_factors': 2, 'dim2_distinct': 0, 'dim2_factors': 0, 'dim3_distinct': 0, 'dim3_factors': 0, 'dim4_distinct': 0, 'dim4_factors': 0, 'dim5_distinct': 0, 'dim5_factors': 0, 'endomorphism_ring_count': 24, 'g': 2, 'galois_groups': ['2T1', '2T1'], 'geom_dim1_distinct': 2, 'geom_dim1_factors': 2, 'geom_dim2_distinct': 0, 'geom_dim2_factors': 0, 'geom_dim3_distinct': 0, 'geom_dim3_factors': 0, 'geom_dim4_distinct': 0, 'geom_dim4_factors': 0, 'geom_dim5_distinct': 0, 'geom_dim5_factors': 0, 'geometric_center_dim': 3, 'geometric_extension_degree': 2, 'geometric_galois_groups': ['1T1', '2T1'], 'geometric_number_fields': ['1.1.1.1', '2.0.152.1'], 'geometric_splitting_field': '2.0.152.1', 'geometric_splitting_polynomials': [[38, 0, 1]], 'group_structure_count': 8, 'has_geom_ss_factor': True, 'has_jacobian': 1, 'has_principal_polarization': 1, 'hyp_count': 180, 'is_geometrically_simple': False, 'is_geometrically_squarefree': True, 'is_primitive': True, 'is_simple': False, 'is_squarefree': True, 'is_supersingular': False, 'jacobian_count': 180, 'label': '2.47.ag_dq', 'max_divalg_dim': 1, 'max_geom_divalg_dim': 4, 'max_twist_degree': 2, 'newton_coelevation': 1, 'newton_elevation': 1, 'number_fields': ['2.0.152.1', '2.0.47.1'], 'p': 47, 'p_rank': 1, 'p_rank_deficit': 1, 'poly': [1, -6, 94, -282, 2209], 'poly_str': '1 -6 94 -282 2209 ', 'primitive_models': [], 'q': 47, 'real_poly': [1, -6], 'simple_distinct': ['1.47.ag', '1.47.a'], 'simple_factors': ['1.47.agA', '1.47.aA'], 'simple_multiplicities': [1, 1], 'singular_primes': ['2,-F+1', '3,4*V-7', '3,-2*V+16'], 'slopes': ['0A', '1/2A', '1/2B', '1A'], 'splitting_field': '4.0.51036736.2', 'splitting_polynomials': [[714, -100, 101, -2, 1]], 'twist_count': 2, 'twists': [['2.47.g_dq', '2.2209.fw_opq', 2]], 'weak_equivalence_count': 28, 'zfv_index': 72, 'zfv_index_factorization': [[2, 3], [3, 2]], 'zfv_is_bass': False, 'zfv_is_maximal': False, 'zfv_plus_index': 1, 'zfv_plus_index_factorization': [], 'zfv_plus_norm': 28576, 'zfv_singular_count': 6, 'zfv_singular_primes': ['2,-F+1', '3,4*V-7', '3,-2*V+16']}
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av_fq_endalg_factors • Show schema
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id: 37709
{'base_label': '2.47.ag_dq', 'extension_degree': 1, 'extension_label': '1.47.ag', 'multiplicity': 1}
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id: 37710
{'base_label': '2.47.ag_dq', 'extension_degree': 1, 'extension_label': '1.47.a', 'multiplicity': 1}
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id: 37711
{'base_label': '2.47.ag_dq', 'extension_degree': 2, 'extension_label': '1.2209.cg', 'multiplicity': 1}
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id: 37712
{'base_label': '2.47.ag_dq', 'extension_degree': 2, 'extension_label': '1.2209.dq', 'multiplicity': 1}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['0', '0'], 'center': '2.0.152.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.47.ag', 'galois_group': '2T1', 'places': [['44', '1'], ['3', '1']]}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['0'], 'center': '2.0.47.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.47.a', 'galois_group': '2T1', 'places': [['23', '1']]}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['0', '0'], 'center': '2.0.152.1', 'center_dim': 2, 'divalg_dim': 1, 'extension_label': '1.2209.cg', 'galois_group': '2T1', 'places': [['44', '1'], ['3', '1']]}
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av_fq_endalg_data • Show schema
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{'brauer_invariants': ['1/2'], 'center': '1.1.1.1', 'center_dim': 1, 'divalg_dim': 4, 'extension_label': '1.2209.dq', 'galois_group': '1T1', 'places': [['0']]}