# Stored data for abelian variety isogeny class 2.19.ad_k, downloaded from the LMFDB on 28 May 2026.
{"abvar_count": 312, "abvar_counts": [312, 134784, 46309536, 17093306880, 6144218674152, 2213192742598656, 799029886390379592, 288443170343851960320, 104126700725360899106976, 37589944905494015471858304], "abvar_counts_str": "312 134784 46309536 17093306880 6144218674152 2213192742598656 799029886390379592 288443170343851960320 104126700725360899106976 37589944905494015471858304 ", "angle_corank": 0, "angle_rank": 2, "angles": [0.20325986418683, 0.651731832911273], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 17, "curve_counts": [17, 373, 6752, 131161, 2481407, 47043286, 893897693, 16983666481, 322685684768, 6131061600853], "curve_counts_str": "17 373 6752 131161 2481407 47043286 893897693 16983666481 322685684768 6131061600853 ", "curves": ["y^2=13*x^6+7*x^5+3*x^4+9*x^3+17*x^2+10*x", "y^2=6*x^5+18*x^4+16*x^3+9*x^2+13*x+16", "y^2=17*x^6+5*x^5+12*x^4+16*x^3+7*x^2+12*x+7", "y^2=15*x^6+16*x^5+5*x^4+12*x^3+17*x^2+5*x+15", "y^2=2*x^6+2*x^5+8*x^4+11*x^3+x^2+x+3", "y^2=17*x^6+14*x^5+12*x^3+16*x^2+5*x+1", "y^2=6*x^6+6*x^5+14*x^4+4*x^3+7*x^2+15*x+10", "y^2=11*x^6+7*x^5+10*x^4+14*x^3+10*x^2+17*x+9", "y^2=4*x^5+4*x^4+4*x^3+14*x^2+9*x+18", "y^2=3*x^6+13*x^5+12*x^4+7*x^3+5*x^2+4*x", "y^2=x^6+x^5+9*x^4+2*x^2+8*x+1", "y^2=x^6+10*x^5+9*x^4+16*x^3+8*x^2+5*x+17", "y^2=6*x^6+10*x^5+7*x^4+14*x^3+2*x^2+17*x+2", "y^2=3*x^6+3*x^5+14*x^4+14*x^3+3*x^2+x+17", "y^2=11*x^6+10*x^5+12*x^4+9*x^3+17*x^2+15*x+4", "y^2=10*x^6+7*x^5+15*x^4+6*x^3+x^2+9*x", "y^2=7*x^6+17*x^5+12*x^4+14*x^3+18*x^2+14*x+4", "y^2=9*x^5+15*x^4+3*x^3+10*x", "y^2=14*x^6+8*x^5+13*x^4+12*x^3+5*x^2+18*x+13", "y^2=5*x^6+10*x^5+4*x^4+6*x^3+8*x+4", "y^2=x^5+14*x^4+14*x^3+10*x^2+8*x+18", "y^2=12*x^6+10*x^5+12*x^4+x^3+18*x+17", "y^2=15*x^6+11*x^5+9*x^4+5*x^3+13*x^2+15*x+15", "y^2=17*x^6+4*x^5+12*x^4+x^3+2*x^2+11*x+18", "y^2=12*x^6+5*x^5+7*x^4+17*x^3+18*x^2+14*x+5", "y^2=17*x^5+8*x^4+11*x^3+16*x^2+9*x+4", "y^2=x^6+3*x^5+11*x^4+6*x^3+6*x^2+4*x+2", "y^2=2*x^5+11*x^4+7*x^3+14*x^2+5*x+17", "y^2=10*x^6+4*x^5+2*x^4+8*x^3+14*x^2+13*x+14", "y^2=13*x^6+4*x^5+10*x^4+7*x^3+11*x^2+13*x+5", "y^2=15*x^6+15*x^5+11*x^4+9*x^3+6*x^2+3*x+16", "y^2=11*x^6+13*x^5+13*x^3+15*x^2+3*x+3"], "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": 8, "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": ["2.0.3.1", "2.0.15.1"], "geometric_splitting_field": "4.0.225.1", "geometric_splitting_polynomials": [[1, 1, 2, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 32, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 32, "label": "2.19.ad_k", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["2.0.3.1", "2.0.15.1"], "p": 19, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -3, 10, -57, 361], "poly_str": "1 -3 10 -57 361 ", "primitive_models": [], "q": 19, "real_poly": [1, -3, -28], "simple_distinct": ["1.19.ah", "1.19.e"], "simple_factors": ["1.19.ahA", "1.19.eA"], "simple_multiplicities": [1, 1], "singular_primes": ["3,V+13", "11,-4*F^2+F+6*V+223", "2,V-7"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.225.1", "splitting_polynomials": [[1, 1, 2, -1, 1]], "twist_count": 12, "twists": [["2.19.al_co", "2.361.l_sm", 2], ["2.19.d_k", "2.361.l_sm", 2], ["2.19.l_co", "2.361.l_sm", 2], ["2.19.d_bi", "2.6859.aee_gsk", 3], ["2.19.m_cs", "2.6859.aee_gsk", 3], ["2.19.am_cs", "2.47045881.advw_advgrkc", 6], ["2.19.af_bq", "2.47045881.advw_advgrkc", 6], ["2.19.ae_g", "2.47045881.advw_advgrkc", 6], ["2.19.ad_bi", "2.47045881.advw_advgrkc", 6], ["2.19.e_g", "2.47045881.advw_advgrkc", 6], ["2.19.f_bq", "2.47045881.advw_advgrkc", 6]], "weak_equivalence_count": 8, "zfv_index": 726, "zfv_index_factorization": [[2, 1], [3, 1], [11, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 1620, "zfv_singular_count": 6, "zfv_singular_primes": ["3,V+13", "11,-4*F^2+F+6*V+223", "2,V-7"]}