# Stored data for abelian variety isogeny class 4.5.a_ak_a_cx, downloaded from the LMFDB on 06 October 2026.
{"abvar_count": 441, "abvar_counts": [441, 194481, 252047376, 179607287601, 95306425775001, 63527879748485376, 37251949328613125001, 23432673552555179690001, 14551945030712127693359376, 9083314794005774963476550001], "abvar_counts_str": "441 194481 252047376 179607287601 95306425775001 63527879748485376 37251949328613125001 23432673552555179690001 14551945030712127693359376 9083314794005774963476550001 ", "angle_corank": 4, "angle_rank": 0, "angles": [0.166666666666667, 0.166666666666667, 0.833333333333333, 0.833333333333333], "center_dim": 4, "curve_count": 6, "curve_counts": [6, 6, 126, 726, 3126, 16626, 78126, 393126, 1953126, 9753126], "curve_counts_str": "6 6 126 726 3126 16626 78126 393126 1953126 9753126 ", "curves": [], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 1, "dim2_factors": 2, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "g": 4, "galois_groups": ["4T2"], "geom_dim1_distinct": 1, "geom_dim1_factors": 4, "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": 1, "geometric_extension_degree": 6, "geometric_galois_groups": ["1T1"], "geometric_number_fields": ["1.1.1.1"], "geometric_splitting_field": "1.1.1.1", "geometric_splitting_polynomials": [[0, 1]], "has_geom_ss_factor": true, "has_jacobian": 0, "has_principal_polarization": 1, "hyp_count": 0, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": false, "is_supersingular": true, "label": "4.5.a_ak_a_cx", "max_divalg_dim": 1, "max_geom_divalg_dim": 4, "max_twist_degree": 120, "newton_coelevation": 0, "newton_elevation": 6, "noncyclic_primes": [3, 7], "number_fields": ["4.0.3600.3"], "p": 5, "p_rank": 0, "p_rank_deficit": 4, "poly": [1, 0, -10, 0, 75, 0, -250, 0, 625], "poly_str": "1 0 -10 0 75 0 -250 0 625 ", "primitive_models": [], "q": 5, "real_poly": [1, 0, -30, 0, 225], "simple_distinct": ["2.5.a_af"], "simple_factors": ["2.5.a_afA", "2.5.a_afB"], "simple_multiplicities": [2], "slopes": ["1/2A", "1/2B", "1/2C", "1/2D", "1/2E", "1/2F", "1/2G", "1/2H"], "splitting_field": "4.0.3600.3", "splitting_polynomials": [[25, 0, -5, 0, 1]], "twist_count": 33, "twists": [["4.5.a_f_a_a", "4.125.a_tg_a_firu", 3], ["4.5.a_u_a_fu", "4.125.a_tg_a_firu", 3], ["4.5.a_a_a_z", "4.625.dw_jgk_ofvk_qghct", 4], ["4.5.a_k_a_cx", "4.625.dw_jgk_ofvk_qghct", 4], ["4.5.a_a_a_az", "4.390625.dse_iogmk_mqubciq_nwyzpwget", 8], ["4.5.a_au_a_fu", "4.244140625.ahcxs_wdjbxpc_abnizdflzfhw_brstyghqcemlus", 12], ["4.5.a_ap_a_dw", "4.244140625.ahcxs_wdjbxpc_abnizdflzfhw_brstyghqcemlus", 12], ["4.5.a_af_a_a", "4.244140625.ahcxs_wdjbxpc_abnizdflzfhw_brstyghqcemlus", 12], ["4.5.a_a_a_aby", "4.244140625.ahcxs_wdjbxpc_abnizdflzfhw_brstyghqcemlus", 12], ["4.5.a_p_a_dw", "4.244140625.ahcxs_wdjbxpc_abnizdflzfhw_brstyghqcemlus", 12], ["4.5.a_af_a_z", "4.30517578125.a_pfecibjg_a_diqdzialpfbabxlu", 15], ["4.5.af_k_az_cx", "4.95367431640625.dhmmtw_gtqvedaneek_iwztgvjwfwcrntfk_irlvrthfekgjlqbctghkt", 20], ["4.5.f_k_z_cx", "4.95367431640625.dhmmtw_gtqvedaneek_iwztgvjwfwcrntfk_irlvrthfekgjlqbctghkt", 20], ["4.5.a_ak_a_by", "4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms", 24], ["4.5.a_af_a_by", "4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms", 24], ["4.5.a_a_a_by", "4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms", 24], ["4.5.a_f_a_by", "4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms", 24], ["4.5.a_k_a_by", "4.59604644775390625.agikaoei_rmsjsdbgbupdc_abbqsulljfxtuxwtrcbie_bbiaogoorycxyqfdcriolzgpms", 24], ["4.5.a_a_a_a", "4.3552713678800500929355621337890625.aezxvixebtceii_kyafsfvmjqtzlrqvwnvjzsgfc_anquiklkseppdjnbabddlssmaetcbfdagvpyoe_kqzwgvtuparacmljwsdltylahvexkiykuhueczvfrwwwslyws", 48], ["4.5.ak_cd_ahs_uf", "4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos", 60], ["4.5.af_f_z_adw", "4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos", 60], ["4.5.af_k_a_az", "4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos", 60], ["4.5.af_u_aby_ev", "4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos", 60], ["4.5.af_z_acx_hs", "4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos", 60], ["4.5.a_f_a_z", "4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos", 60], ["4.5.f_f_az_adw", "4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos", 60], ["4.5.f_k_a_az", "4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos", 60], ["4.5.f_u_by_ev", "4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos", 60], ["4.5.f_z_cx_hs", "4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos", 60], ["4.5.k_cd_hs_uf", "4.867361737988403547205962240695953369140625.aelmwqkrycybitwps_iqlwgmqaqksatftwplxmzsewurprftc_ajpgxbrhuvpwkbrowfvuwwzbpemlvhodjxzvctzvrgbfkvw_gragsnsjuxkzjowjzzkdkrueuwiybivgszadyflkdtqxbjvrdksnqxbzaheos", 60], ["4.5.af_p_az_by", "4.752316384526264005099991383822237233803945956334136013765601092018187046051025390625.acmdkbwepaziwmxyglvzhlbmnymlxmui_crfhxahjdeekdvodzztqzbxrnodovisxmuklzhjtrcreaoirgorvboleuxrlc_abqrnlwxmsgohcbgmdkovzjthpuitbdxgpqfoijpqioaxuflewyvfifqxsazggvenizehgdcbrhouzwgvkeingwvqsge_qlptvaurceumrqpyusgqoshzpizdndgyhomthtmjnpmxezaialslexnnazdgjudtjxggxgtmpurretwbaeyejbdvzvddapebfkqgtyhhoumpmppryltjeras", 120], ["4.5.f_p_z_by", "4.752316384526264005099991383822237233803945956334136013765601092018187046051025390625.acmdkbwepaziwmxyglvzhlbmnymlxmui_crfhxahjdeekdvodzztqzbxrnodovisxmuklzhjtrcreaoirgorvboleuxrlc_abqrnlwxmsgohcbgmdkovzjthpuitbdxgpqfoijpqioaxuflewyvfifqxsazggvenizehgdcbrhouzwgvkeingwvqsge_qlptvaurceumrqpyusgqoshzpizdndgyhomthtmjnpmxezaialslexnnazdgjudtjxggxgtmpurretwbaeyejbdvzvddapebfkqgtyhhoumpmppryltjeras", 120]]}