# Stored data for abelian variety isogeny class 2.73.aj_i, downloaded from the LMFDB on 18 February 2026.
{"abvar_count": 4672, "abvar_counts": [4672, 28050688, 150370226176, 806277418988544, 4297557896221229632, 22901816648265382297600, 122044964452038132126971968, 650377867387845250999541551104, 3465863666635204928622401928269824, 18469587758931442496658857701293468928], "abvar_counts_str": "4672 28050688 150370226176 806277418988544 4297557896221229632 22901816648265382297600 122044964452038132126971968 650377867387845250999541551104 3465863666635204928622401928269824 18469587758931442496658857701293468928 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.00989864991722457, 0.656768016749442], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 65, "curve_counts": [65, 5265, 386534, 28391809, 2073038825, 151332697230, 11047394030465, 806460076481089, 58871585775493622, 4297625826631221825], "curve_counts_str": "65 5265 386534 28391809 2073038825 151332697230 11047394030465 806460076481089 58871585775493622 4297625826631221825 ", "curves": ["y^2=12*x^6+x^5+13*x^4+68*x^3+19*x^2+39*x+33", "y^2=51*x^6+56*x^5+7*x^4+49*x^3+22*x^2+44*x+69", "y^2=20*x^6+49*x^5+37*x^4+49*x^3+31*x^2+53*x+63", "y^2=34*x^6+6*x^5+67*x^4+41*x^3+56*x^2+25*x+2", "y^2=3*x^6+44*x^5+10*x^4+9*x^3+23*x^2+25*x+37", "y^2=58*x^6+57*x^5+33*x^4+16*x^3+x^2+17*x+46", "y^2=26*x^6+14*x^5+22*x^4+8*x^3+41*x^2+5*x+29", "y^2=45*x^6+7*x^5+60*x^4+50*x^3+72*x^2+16*x+16", "y^2=62*x^6+54*x^5+12*x^4+38*x^3+34*x^2+52*x+53", "y^2=41*x^6+9*x^5+71*x^4+64*x^3+4*x^2+65*x+6", "y^2=55*x^6+12*x^5+30*x^4+34*x^3+70*x^2+59*x+19", "y^2=51*x^6+37*x^5+10*x^4+44*x^3+9*x^2+42*x+63", "y^2=39*x^6+25*x^5+39*x^4+21*x^3+22*x^2+5*x+13", "y^2=27*x^6+64*x^5+2*x^4+8*x^3+16*x^2+23*x+2", "y^2=40*x^6+13*x^5+70*x^4+52*x^3+72*x^2+23*x"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 1, "dim2_factors": 1, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 0, "dim4_factors": 0, "dim5_distinct": 0, "dim5_factors": 0, "endomorphism_ring_count": 4, "g": 2, "galois_groups": ["4T2"], "geom_dim1_distinct": 1, "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": 2, "geometric_extension_degree": 3, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.211.1"], "geometric_splitting_field": "2.0.211.1", "geometric_splitting_polynomials": [[53, -1, 1]], "group_structure_count": 4, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 15, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 15, "label": "2.73.aj_i", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.400689.1"], "p": 73, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 13, 1, 6]], "poly": [1, -9, 8, -657, 5329], "poly_str": "1 -9 8 -657 5329 ", "primitive_models": [], "principal_polarization_count": 15, "q": 73, "real_poly": [1, -9, -138], "simple_distinct": ["2.73.aj_i"], "simple_factors": ["2.73.aj_iA"], "simple_multiplicities": [1], "singular_primes": ["2,F-2*V+21"], "size": 15, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.400689.1", "splitting_polynomials": [[2809, -53, -52, -1, 1]], "twist_count": 6, "twists": [["2.73.j_i", "2.5329.acn_abqm", 2], ["2.73.s_it", "2.389017.adro_fcavu", 3], ["2.73.as_it", "2.151334226289.adizya_eglxizuhy", 6], ["2.73.a_cn", "2.151334226289.adizya_eglxizuhy", 6], ["2.73.j_i", "2.151334226289.adizya_eglxizuhy", 6], ["2.73.a_acn", "2.22902048046490258711521.acseryapke_cwrjdymghctcpqkeg", 12]], "weak_equivalence_count": 4, "zfv_index": 8, "zfv_index_factorization": [[2, 3]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 6, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 64, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F-2*V+21"]}