# Stored data for abelian variety isogeny class 4.5.d_ab_ad_q, downloaded from the LMFDB on 16 April 2026.
{"abvar_count": 976, "abvar_counts": [976, 249856, 306445456, 148334510080, 93154617968896, 60951049991704576, 37697104136965345936, 23382391377902546452480, 14557764104761392701014096, 9087224972844505122645999616], "abvar_counts_str": "976 249856 306445456 148334510080 93154617968896 60951049991704576 37697104136965345936 23382391377902546452480 14557764104761392701014096 9087224972844505122645999616 ", "angle_corank": 2, "angle_rank": 2, "angles": [0.144130581889375, 0.417838834988402, 0.817838834988402, 0.944130581889375], "center_dim": 8, "curve_count": 9, "curve_counts": [9, 15, 153, 607, 3054, 15975, 79053, 392287, 1953909, 9757330], "curve_counts_str": "9 15 153 607 3054 15975 79053 392287 1953909 9757330 ", "curves": ["y^2=x^9+x^7+4*x^6+2*x^5+x^4+4*x^3+4*x^2+2*x+1", "y^2=x^10+2*x^8+4*x^7+x^6+3*x^4+2*x^3+3*x^2+4*x", "y^2=x^10+x^9+4*x^8+3*x^7+x^6+x^4+4*x^3+4*x^2+2*x+4"], "dim1_distinct": 0, "dim1_factors": 0, "dim2_distinct": 0, "dim2_factors": 0, "dim3_distinct": 0, "dim3_factors": 0, "dim4_distinct": 1, "dim4_factors": 1, "dim5_distinct": 0, "dim5_factors": 0, "g": 4, "galois_groups": ["8T10"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 2, "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": 5, "geometric_galois_groups": ["4T3"], "geometric_number_fields": ["4.0.8525.1"], "geometric_splitting_field": "4.0.8525.1", "geometric_splitting_polynomials": [[25, -5, 9, -1, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 3, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "label": "4.5.d_ab_ad_q", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 30, "newton_coelevation": 6, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["8.0.1816890625.4"], "p": 5, "p_rank": 4, "p_rank_deficit": 0, "poly": [1, 3, -1, -3, 16, -15, -25, 375, 625], "poly_str": "1 3 -1 -3 16 -15 -25 375 625 ", "primitive_models": [], "q": 5, "real_poly": [1, 3, -21, -48, 76], "simple_distinct": ["4.5.d_ab_ad_q"], "simple_factors": ["4.5.d_ab_ad_qA"], "simple_multiplicities": [1], "slopes": ["0A", "0B", "0C", "0D", "1A", "1B", "1C", "1D"], "splitting_field": "8.0.1816890625.4", "splitting_polynomials": [[625, -250, -25, -40, 41, -8, -1, -2, 1]], "twist_count": 10, "twists": [["4.5.ad_ab_d_q", "4.25.al_bz_ab_abee", 2], ["4.5.ac_ab_ai_bp", "4.3125.acu_achw_agyyy_cmxuta", 5], ["4.5.ac_t_abc_fl", "4.3125.acu_achw_agyyy_cmxuta", 5], ["4.5.a_r_a_er", "4.9765625.amhc_dspczs_axzwgswdc_fakugxwfsne", 10], ["4.5.c_ab_i_bp", "4.9765625.amhc_dspczs_axzwgswdc_fakugxwfsne", 10], ["4.5.c_t_bc_fl", "4.9765625.amhc_dspczs_axzwgswdc_fakugxwfsne", 10], ["4.5.b_ai_ab_bz", "4.30517578125.acjgfg_cqzbkdvqa_abvseyhpvenqui_wbourbezhwzcjdnq", 15], ["4.5.a_ar_a_er", "4.95367431640625.bqolxg_berjfpamrom_bnpmzclmepdniupc_bwyrscunfsrcimmszbzkg", 20], ["4.5.ab_ai_b_bz", "4.931322574615478515625.agibgiedk_cjagunkrkqjmgwpo_ajsehcqdlwamlajpsbaamcya_cadyfmusaznelnekhcbspkdaxxavbus", 30]]}