Table belyi_galmaps
Belyi maps
{'BelyiDB_label': '6T15-[5,5,4]-51-51-42-g1-a', 'BelyiDB_plabel': '6T15-[5,5,4]-51-51-42-g1', 'a_s': 4, 'abc': [5, 5, 4], 'aut_group': [[1, 2, 3, 4, 5, 6]], 'b_s': 5, 'base_field': [16, 0, -2, 0, 1], 'base_field_label': '4.0.14400.3', 'c_s': 5, 'curve': 'y^2=x^3+1/295245000*(187132*nu^3-52599*nu^2-1245024*nu-2424448)*x+1/16142520375000*(3341164270*nu^3-5720990089*nu^2-38301326128*nu-65046518024)', 'deg': 6, 'embeddings': [[1.58113883008419, 1.224744871391589], [-1.58113883008419, 1.224744871391589], [-1.58113883008419, -1.224744871391589], [1.58113883008419, -1.224744871391589]], 'friends': [], 'g': 1, 'geomtype': 'H', 'group': '6T15', 'group_num': 15, 'id': 75, 'is_primitive': True, 'label': '6T15-5.1_5.1_4.2-a', 'lambdas': [[5, 1], [5, 1], [4, 2]], 'map': '(1/61509375*(-348496*nu^3-741120*nu^2-220032*nu+1325056)*x^2+1/1121008359375*(-1779172576*nu^3-7720954976*nu^2-13551312128*nu-8754475264)*x+1/6810125783203125*(2876788492172*nu^3-5968135269264*nu^2-36027973300704*nu-60005055586688))/(x^6+1/12150*(-478*nu^3-575*nu^2+880*nu-3124)*x^5+1/59049000*(-220348*nu^3+430695*nu^2+3479136*nu+9690880)*x^4+1/1614252037500*(-1960623166*nu^3-5800744319*nu^2-10636114256*nu-1393134520)*x^3+1/26150883007500000*(-16499085466792*nu^3+36659243012625*nu^2+213540923222592*nu+352327034626936)*x^2+1/2382999214058437500000*(811866697332031226*nu^3+1370168723740622515*nu^2-538453590192224528*nu-4790319774148953016)*x+1/173720642704860093750000000*(-321238464333470237716*nu^3-4302581215060946019141*nu^2-11678312737214932209888*nu-13146805620882796103864))*y+(1/61509375*(348496*nu^3+741120*nu^2+220032*nu-1325056)*x^3+1/373669453125*(-469645192*nu^3+437700016*nu^2+4180837696*nu+7636429952)*x^2+1/11350209638671875*(-852829887316*nu^3+1270879441200*nu^2+9158542172448*nu+15867682562176)*x+1/620572711994384765625*(-79784546770981598*nu^3-156472493857022308*nu^2-16062883459261264*nu+383429587505849248))/(x^6+1/12150*(-478*nu^3-575*nu^2+880*nu-3124)*x^5+1/59049000*(-220348*nu^3+430695*nu^2+3479136*nu+9690880)*x^4+1/1614252037500*(-1960623166*nu^3-5800744319*nu^2-10636114256*nu-1393134520)*x^3+1/26150883007500000*(-16499085466792*nu^3+36659243012625*nu^2+213540923222592*nu+352327034626936)*x^2+1/2382999214058437500000*(811866697332031226*nu^3+1370168723740622515*nu^2-538453590192224528*nu-4790319774148953016)*x+1/173720642704860093750000000*(-321238464333470237716*nu^3-4302581215060946019141*nu^2-11678312737214932209888*nu-13146805620882796103864))', 'orbit_size': 4, 'pass_size': 8, 'plabel': '6T15-5.1_5.1_4.2', 'plane_constant': '1/36*(-25*nu^2 + 25)', 'plane_map_constant_factored': '\\frac{2^{2} \\cdot 3}{5^{3}}(\\nu^{2} - 1)', 'plane_model': '(-2)*t^2 + (18*x^4 + (-3*nu^3 - 12*nu^2 + 30*nu - 16)*x^3 + (-12*nu^3 + 23*nu^2 - 48*nu + 7)*x^2 + 1/4*(69*nu^3 - 140*nu^2 - 42*nu + 272)*x + 1/2*(-12*nu^3 + 13*nu^2 + 32*nu - 128))*t + x^5*(x + 1/4*(-3*nu^3 - 4*nu^2 + 6*nu + 16))', 'primitivization': '6T15-5.1_5.1_4.2-a', 'triples': [[[3, 1, 4, 5, 2, 6], [3, 2, 5, 1, 6, 4], [2, 3, 4, 1, 6, 5]], [[2, 4, 3, 5, 6, 1], [2, 6, 1, 3, 5, 4], [2, 3, 4, 1, 6, 5]], [[3, 2, 4, 5, 6, 1], [3, 6, 2, 1, 5, 4], [2, 3, 4, 1, 6, 5]], [[2, 4, 5, 3, 1, 6], [2, 5, 1, 4, 6, 3], [2, 3, 4, 1, 6, 5]]], 'triples_cyc': [['(1,3,4,5,2)', '(1,3,5,6,4)', '(1,2,3,4)(5,6)'], ['(1,2,4,5,6)', '(1,2,6,4,3)', '(1,2,3,4)(5,6)'], ['(1,3,4,5,6)', '(1,3,2,6,4)', '(1,2,3,4)(5,6)'], ['(1,2,4,3,5)', '(1,2,5,6,3)', '(1,2,3,4)(5,6)']]}