# Stored data for abelian variety isogeny class 3.16.ag_g_br, downloaded from the LMFDB on 12 October 2026.
{"abvar_count": 2700, "abvar_counts": [2700, 15384600, 69087330000, 285418945350000, 1152124171115017500, 4724318383516892160000, 19342267874900362053663300, 79227926982368874371069100000, 324523536646418245932859719630000, 1329229466775962992864497630733515000], "abvar_counts_str": "2700 15384600 69087330000 285418945350000 1152124171115017500 4724318383516892160000 19342267874900362053663300 79227926982368874371069100000 324523536646418245932859719630000 1329229466775962992864497630733515000 ", "angle_corank": 1, "angle_rank": 2, "angles": [0.126773578991898, 0.285098958591725, 0.793440245658565], "center_dim": 6, "cohen_macaulay_max": 2, "curve_count": 11, "curve_counts": [11, 233, 4118, 66449, 1047851, 16784150, 268427891, 4294954529, 68720531918, 1099512844553], "curve_counts_str": "11 233 4118 66449 1047851 16784150 268427891 4294954529 68720531918 1099512844553 ", "curves": ["y^2+(a^2*x^4+a*x)*y=x^3+(a^2+a+1)*x^2+(a^3+a+1)*x+1", "y^2+(a^2*x^4+a*x)*y=(a^2+1)*x^3+(a+1)*x^2+(a^2+1)*x+a^3+a^2+a", "y^2+(a^3*x^4+a*x)*y=(a+1)*x^3+(a^3+a^2)*x^2+(a^3+a)*x+a^2+a+1", "y^2+(a^3*x^4+a*x)*y=(a^2+1)*x^3+a^3*x^2+a^2*x+a^2+1", "y^2+(a*x^4+a*x^3+a*x)*y=x^8+x^3+(a+1)*x^2+a^2*x+a^3+a^2+a", "y^2+(a*x^4+a*x^3+a*x)*y=x^8+a*x^3+a^2*x^2+a^2*x+1", "y^2+(a*x^4+a*x^3+a*x)*y=x^8+a*x^3+(a^2+a+1)*x^2+(a^2+1)*x+1", "y^2+(a*x^4+a*x^3+a*x)*y=x^8+a*x^3+(a^3+a+1)*x^2+a^3+a^2+a", "y^2+(a*x^4+a*x^3+a*x)*y=x^8+a*x^3+(a^3+a^2)*x^2+(a^3+a)*x+a^3+a^2+a", "y^2+(a*x^4+a*x^3+a*x)*y=x^8+(a^2+1)*x^3+a^3*x^2+1", "y^2+(a*x^4+a*x^3+a*x)*y=x^8+(a^2+a)*x^3+(a^3+1)*x+a^3+1", "y^2+(a*x^4+a*x^3+a*x)*y=x^8+(a^2+a)*x^3+(a+1)*x^2+(a^3+a^2+a+1)*x+a", "y^2+(a*x^4+a*x^3+a*x)*y=x^8+(a^2+a)*x^3+a^3*x^2+(a^3+a+1)*x+a^3+1", "y^2+(a*x^4+a*x^3+a*x)*y=x^8+(a^2+a)*x^3+(a^3+a^2+a+1)*x^2+a*x+a", "y^2+(a*x^4+a*x^3+a*x)*y=x^8+(a^3+a)*x^3+(a^3+a+1)*x^2+(a^3+a^2+a+1)*x+a^3+1", "y^2+(a*x^4+a*x^3+a*x)*y=x^8+(a^3+a^2+a)*x^3+a^2*x^2+(a^3+a+1)*x+a", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a^2*x^3+(a^2+a+1)*x^2+a*x+a", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a^2*x^3+(a^2+a+1)*x^2+(a+1)*x+a+1", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=(a^2+a)*x^3+(a^2+a+1)*x^2+a^3*x+a^3+a^2+a", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=(a^2+a)*x^3+(a^3+a+1)*x^2+x+a", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=(a^3+a^2+a)*x^3+(a^3+a^2)*x", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+a^3*x^2+(a^3+a^2+a+1)*x", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+x^3+(a+1)*x^2+a^3*x+a^3+a", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+x^3+a^2*x^2+(a^2+a)*x+a^3+a^2", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+(a+1)*x^3+x+a+1", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+(a+1)*x^3+(a^2+a+1)*x^2+(a^3+a+1)*x+a^2+a", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+(a^2+1)*x^3+a^3*x^2+(a^3+a^2+1)*x+a^3+a+1", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+(a^2+a)*x^3+a^3*x^2+(a^2+1)*x+a^3+a+1", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+(a^2+a)*x^3+(a^3+a^2+a+1)*x^2+(a^3+a^2+a)*x+a^3+a^2+a", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+(a^2+a+1)*x^3+(a^3+a+1)*x^2+(a^3+a^2+a+1)*x+a+1", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+(a^2+a+1)*x^3+(a^3+a^2)*x^2+(a^3+a^2)*x+a", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+(a^3+1)*x^3+(a^2+a+1)*x^2+(a^3+1)*x+a^2+a", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+(a^3+a^2)*x^3+a^2*x^2+(a+1)*x", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+(a^3+a^2+a)*x^3+(a+1)*x^2+x+a^3+a^2", "y^2+((a^3+1)*x^4+a*x^3+a*x)*y=a*x^8+(a^3+a^2+a+1)*x^3+a^2*x^2+(a^3+1)*x+a^2+1", "y^2+(x^4+a*x^3+a*x)*y=a^2*x^3+(a^3+a^2)*x^2+a^3*x+a^3", "y^2+(x^4+a*x^3+a*x)*y=a^2*x^3+(a^3+a^2)*x^2+(a^3+a)*x+a^3+a", "y^2+(x^4+a*x^3+a*x)*y=(a^3+1)*x^3+(a+1)*x", "y^2+(x^4+a*x^3+a*x)*y=(a^3+a^2+a)*x^3+(a^3+a^2)*x^2+(a^2+a+1)*x+a^3+1", "y^2+(x^4+a*x^3+a*x)*y=(a^3+a^2+a)*x^3+(a^3+a^2+a+1)*x^2+a*x+a^3+a", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+x^3+(a^2+a+1)*x^2+a*x+a^2+a", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+a*x^3+(a^3+a^2)*x^2+(a^2+a)*x+a^2+a+1", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+a^2*x^3+(a^3+a^2)*x^2+(a^3+a^2)*x+a^3", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+(a^2+a)*x^3+(a+1)*x^2+a^2+1", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+(a^2+a)*x^3+(a^3+a^2+a+1)*x^2+(a^3+1)*x+a^3+a+1", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+(a^2+a+1)*x^3+(a^3+a^2+a+1)*x^2+(a^3+a^2+a+1)*x+a^3", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+a^3*x^3+a^2*x^2+(a^3+a^2)*x", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+a^3*x^3+a^3*x^2+a^2*x+a", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+(a^3+a)*x^3+(a^3+a^2+a)*x+1", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+(a^3+a)*x^3+(a^3+a^2)*x^2+x+a^2+a+1", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+(a^3+a^2)*x^3+(a^2+a+1)*x^2+a^3*x+a^2+a", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+(a^3+a^2)*x^3+(a^3+a+1)*x^2+(a^2+1)*x", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+(a^3+a^2+1)*x^3+(a+1)*x^2+(a^2+1)*x+a^3+a+1", "y^2+(x^4+a*x^3+a*x)*y=a^3*x^8+(a^3+a^2+a+1)*x^3+(a^3+a^2+a+1)*x^2+a*x+a^3+a^2+a", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=a^2*x^3+(a+1)*x^2+(a^2+a+1)*x+a^2+a+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=a^2*x^3+(a+1)*x^2+(a^3+a^2+1)*x+a^3+a^2+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=(a^2+1)*x^3+a^3*x", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=(a^3+1)*x^3+(a+1)*x^2+(a^3+a^2)*x+a^2+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=(a^3+1)*x^3+(a^3+a+1)*x^2+(a^3+a)*x+a^3+a^2+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+(a+1)*x^2+a^3*x+a^3", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+x^3+(a^3+a+1)*x^2+(a^3+a^2)*x+a^3+a^2+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+(a^2+1)*x^3+a*x+a^2+a+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+(a^2+1)*x^3+(a+1)*x^2+(a^2+a+1)*x+a^3+a^2+a", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+(a^2+a)*x^3+a^3*x^2+(a^3+a+1)*x+a+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+(a^2+a)*x^3+(a^3+a+1)*x^2+a^3+a^2+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+(a^2+a+1)*x^3+(a+1)*x^2+(a^3+1)*x+a^2+a", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+a^3*x^3+a^2*x^2+(a^2+1)*x+a^3+a^2+a+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+a^3*x^3+(a^2+a+1)*x^2+a^2*x+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+(a^3+1)*x^3+a^2*x^2+a^3*x+a^3+a^2+a+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+(a^3+a)*x^3+a^2*x+a^3+a^2+a", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+(a^3+a^2)*x^3+(a^3+a^2)*x^2+x+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+(a^3+a^2)*x^3+(a^3+a^2+a+1)*x^2+(a^2+a)*x+a^3+a+1", "y^2+((a^2+1)*x^4+a*x^3+a*x)*y=x^8+(a^3+a^2+a+1)*x^3+(a^3+a+1)*x^2+x+a^2+a", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=a^2*x^3+a^3*x^2+x+1", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=a^2*x^3+a^3*x^2+(a^3+a^2)*x+a^3+a^2", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=(a^2+1)*x^3+a^3*x^2+(a+1)*x+a^2+a", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=(a^2+1)*x^3+(a^3+a^2+a+1)*x^2+(a^3+a^2+1)*x+1", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=(a^2+a)*x^3+(a^2+a+1)*x", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+(a+1)*x^2+(a^3+a+1)*x", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+(a^2+1)*x^3+(a+1)*x^2+(a^3+1)*x+a^3+a^2+a+1", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+(a^2+1)*x^3+(a^3+a+1)*x^2+(a^2+a)*x+a^2+a", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+(a^2+a)*x^3+(a^3+a^2)*x^2+(a^3+a^2+1)*x+a^2+a+1", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+(a^2+a+1)*x^3+a^2*x^2+(a^3+a^2)*x", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+a^3*x^3+(a^2+a+1)*x^2+(a^2+a+1)*x+1", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+a^3*x^3+(a^3+a^2+a+1)*x^2+(a^3+a+1)*x+a^3+a^2", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+(a^3+1)*x^3+(a+1)*x^2+(a^3+a)*x+a^3+a^2+a+1", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+(a^3+a+1)*x^3+a^2*x^2+(a^3+a^2+a)*x+a^3+1", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+(a^3+a^2)*x^3+(a^3+a^2+1)*x+a^3+a^2", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+(a^3+a^2)*x^3+a^3*x^2+(a^3+a^2+a+1)*x+a^2+1", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+(a^3+a^2+1)*x^3+a^2*x^2+(a^2+1)*x+a^2+a+1", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+(a^3+a^2+1)*x^3+(a^3+a^2)*x^2+(a+1)*x+a", "y^2+((a^3+a^2+a+1)*x^4+a*x^3+a*x)*y=x^8+(a^3+a^2+a)*x^3+a^3*x^2+(a^3+a^2+a)*x+a^2+1"], "dim1_distinct": 1, "dim1_factors": 1, "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": 48, "g": 3, "galois_groups": ["2T1", "4T2"], "geom_dim1_distinct": 2, "geom_dim1_factors": 3, "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": 3, "geometric_galois_groups": ["2T1", "2T1"], "geometric_number_fields": ["2.0.39.1", "2.0.7.1"], "geometric_splitting_field": "4.0.74529.3", "geometric_splitting_polynomials": [[64, 0, 23, 0, 1]], "group_structure_count": 6, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 92, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "label": "3.16.ag_g_br", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 4, "newton_elevation": 0, "noncyclic_primes": [3, 5], "number_fields": ["2.0.39.1", "4.0.441.1"], "p": 2, "p_rank": 3, "p_rank_deficit": 0, "poly": [1, -6, 6, 43, 96, -1536, 4096], "poly_str": "1 -6 6 43 96 -1536 4096 ", "primitive_models": [], "q": 16, "real_poly": [1, -6, -42, 235], "simple_distinct": ["1.16.af", "2.16.ab_ap"], "simple_factors": ["1.16.afA", "2.16.ab_apA"], "simple_multiplicities": [1, 1], "singular_primes": ["3,6*F+V^2+2*V-24", "5,6*F^2-7*F-V^2+25*V-23"], "slopes": ["0A", "0B", "0C", "1A", "1B", "1C"], "splitting_field": "8.0.5554571841.1", "splitting_polynomials": [[625, 0, 75, 0, -16, 0, 3, 0, 1]], "twist_count": 12, "twists": [["3.16.ae_ae_ed", "3.256.ay_bcq_aqer", 2], ["3.16.e_ae_aed", "3.256.ay_bcq_aqer", 2], ["3.16.g_g_abr", "3.256.ay_bcq_aqer", 2], ["3.16.ad_bn_adx", "3.4096.v_flv_yghf", 3], ["3.16.ah_ch_aiv", "3.16777216.kgr_cerudn_gnwejrud", 6], ["3.16.af_bv_afz", "3.16777216.kgr_cerudn_gnwejrud", 6], ["3.16.d_bn_dx", "3.16777216.kgr_cerudn_gnwejrud", 6], ["3.16.f_bv_fz", "3.16777216.kgr_cerudn_gnwejrud", 6], ["3.16.g_g_abr", "3.16777216.kgr_cerudn_gnwejrud", 6], ["3.16.h_ch_iv", "3.16777216.kgr_cerudn_gnwejrud", 6], ["3.16.af_ap_fz", "3.281474976710656.ietzx_ftreewextip_bhhdtegmcoqtujdn", 12], ["3.16.f_ap_afz", "3.281474976710656.ietzx_ftreewextip_bhhdtegmcoqtujdn", 12]], "weak_equivalence_count": 70, "zfv_index": 98415, "zfv_index_factorization": [[3, 9], [5, 1]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_plus_index": 3, "zfv_plus_index_factorization": [[3, 1]], "zfv_plus_norm": 8775, "zfv_singular_count": 4, "zfv_singular_primes": ["3,6*F+V^2+2*V-24", "5,6*F^2-7*F-V^2+25*V-23"]}