# Stored data for abelian variety isogeny class 2.43.au_hd, downloaded from the LMFDB on 27 March 2026.
{"abvar_count": 1155, "abvar_counts": [1155, 3366825, 6362904240, 11709228155625, 21617054566459275, 39960412505483500800, 73885299115126949716035, 136613956401308377622255625, 252599312098782709576723635120, 467056164100957380764190681545625], "abvar_counts_str": "1155 3366825 6362904240 11709228155625 21617054566459275 39960412505483500800 73885299115126949716035 136613956401308377622255625 252599312098782709576723635120 467056164100957380764190681545625 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.183291501244178, 0.259258415260951], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 24, "curve_counts": [24, 1820, 80028, 3424948, 147046344, 6321486710, 271818396888, 11688194346148, 502592569208964, 21611482143169100], "curve_counts_str": "24 1820 80028 3424948 147046344 6321486710 271818396888 11688194346148 502592569208964 21611482143169100 ", "curves": ["y^2=13*x^6+19*x^5+16*x^4+31*x^3+40*x^2+22*x+15", "y^2=7*x^6+6*x^5+32*x^4+30*x^3+33*x^2+11*x+26", "y^2=6*x^6+19*x^5+37*x^4+29*x^3+12*x^2+33*x+38", "y^2=38*x^6+34*x^5+33*x^4+x^3+33*x^2+34*x+38", "y^2=30*x^6+25*x^5+38*x^4+28*x^3+15*x^2+10*x+7", "y^2=30*x^6+22*x^5+20*x^4+32*x^3+18*x^2+29*x+18", "y^2=41*x^6+2*x^5+10*x^4+33*x^3+13*x^2+18*x+11", "y^2=30*x^6+23*x^5+40*x^4+28*x^3+6*x^2+6*x+18", "y^2=33*x^6+20*x^5+14*x^4+23*x^3+16*x^2+27*x+3", "y^2=32*x^6+33*x^5+26*x^4+18*x^3+2*x^2+32*x+8", "y^2=8*x^6+12*x^5+39*x^4+31*x^3+19*x^2+2*x+8", "y^2=29*x^6+39*x^5+18*x^4+3*x^3+2*x^2+18*x+7"], "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": 2, "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": 4, "geometric_extension_degree": 1, "geometric_galois_groups": ["2T1", "2T1"], "geometric_number_fields": ["2.0.51.1", "2.0.91.1"], "geometric_splitting_field": "4.0.21538881.1", "geometric_splitting_polynomials": [[100, 0, 71, 0, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 12, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 12, "label": "2.43.au_hd", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["2.0.51.1", "2.0.91.1"], "p": 43, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 2], [1, 5, 1, 6], [2, 5, 1, 6]], "poly": [1, -20, 185, -860, 1849], "poly_str": "1 -20 185 -860 1849 ", "primitive_models": [], "principal_polarization_count": 16, "q": 43, "real_poly": [1, -20, 99], "simple_distinct": ["1.43.al", "1.43.aj"], "simple_factors": ["1.43.alA", "1.43.ajA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,F+3*V-37"], "size": 16, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.21538881.1", "splitting_polynomials": [[100, 0, 71, 0, 1]], "twist_count": 4, "twists": [["2.43.ac_an", "2.1849.abe_ffn", 2], ["2.43.c_an", "2.1849.abe_ffn", 2], ["2.43.u_hd", "2.1849.abe_ffn", 2]], "weak_equivalence_count": 2, "zfv_index": 4, "zfv_index_factorization": [[2, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 12, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 4641, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F+3*V-37"]}