# Stored data for abelian variety isogeny class 2.61.ax_jj, downloaded from the LMFDB on 01 May 2024.
{"label": "2.61.ax_jj", "g": 2, "p": 61, "q": 61, "poly": [1, -23, 243, -1403, 3721], "poly_str": "1 -23 243 -1403 3721 ", "slopes": ["0A", "0B", "1A", "1B"], "p_rank": 2, "p_rank_deficit": 0, "angles": [0.1001236185759, 0.325377247673571], "angle_rank": 2, "number_fields": ["4.0.103725.1"], "galois_groups": ["4T3"], "center_dim": 4, "abvar_counts": [2539, 13687749, 51609046975, 191735811639909, 713323953851741584, 2654333127751981720725, 9876831941292082696519399, 36751699849411909102984461189, 136753057714148488033980283701475, 508858111666530911649343397895062784], "abvar_counts_str": "2539 13687749 51609046975 191735811639909 713323953851741584 2654333127751981720725 9876831941292082696519399 36751699849411909102984461189 136753057714148488033980283701475 508858111666530911649343397895062784 ", "abvar_count": 2539, "curve_counts": [39, 3679, 227373, 13847899, 844573854, 51520066783, 3142742647629, 191707344257299, 11694146509589703, 713342914532262454], "curve_counts_str": "39 3679 227373 13847899 844573854 51520066783 3142742647629 191707344257299 11694146509589703 713342914532262454 ", "curve_count": 39, "has_jacobian": 1, "has_principal_polarization": 1, "geometric_extension_degree": 1, "geometric_center_dim": 4, "geometric_number_fields": ["4.0.103725.1"], "geometric_galois_groups": ["4T3"], "primitive_models": [], "is_primitive": true, "twists": [["2.61.x_jj", "2.3721.abr_cxd", 2]], "twist_count": 2, "max_twist_degree": 2, "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "is_simple": true, "is_geometrically_simple": true, "simple_distinct": ["2.61.ax_jj"], "simple_multiplicities": [1], "simple_factors": ["2.61.ax_jjA"], "dim1_factors": 0, "dim2_factors": 1, "dim3_factors": 0, "dim4_factors": 0, "dim5_factors": 0, "dim1_distinct": 0, "dim2_distinct": 1, "dim3_distinct": 0, "dim4_distinct": 0, "dim5_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_factors": 1, "geom_dim3_factors": 0, "geom_dim4_factors": 0, "geom_dim5_factors": 0, "geom_dim1_distinct": 0, "geom_dim2_distinct": 1, "geom_dim3_distinct": 0, "geom_dim4_distinct": 0, "geom_dim5_distinct": 0, "has_geom_ss_factor": false, "real_poly": [1, -23, 121], "jacobian_count": 24, "curves": ["y^2=17*x^6+15*x^5+4*x^4+8*x^3+28*x^2+13*x+28", "y^2=46*x^6+48*x^5+35*x^4+27*x^3+55*x^2+20*x+13", "y^2=21*x^6+9*x^5+33*x^4+43*x^3+3*x^2+24*x+8", "y^2=31*x^6+23*x^5+38*x^4+49*x^3+34*x^2+14*x+10", "y^2=26*x^6+19*x^5+6*x^4+27*x^3+49*x^2+19*x+47", "y^2=40*x^6+56*x^5+40*x^4+17*x^3+6*x^2+27*x+31", "y^2=44*x^6+33*x^5+35*x^4+46*x^3+34*x^2+33*x+17", "y^2=23*x^6+39*x^5+28*x^4+2*x^3+30*x^2+36*x+33", "y^2=33*x^6+33*x^5+59*x^4+19*x^3+34*x^2+38*x+8", "y^2=55*x^6+22*x^5+36*x^4+54*x^3+20*x^2+35*x+18", "y^2=17*x^6+36*x^5+14*x^4+11*x^3+57*x^2+43*x+55", "y^2=2*x^6+20*x^5+48*x^4+19*x^3+53*x^2+7*x+10", "y^2=53*x^6+24*x^5+33*x^4+47*x^3+43*x^2+59*x+39", "y^2=54*x^6+22*x^5+53*x^4+57*x^3+18*x^2+16*x+55", "y^2=56*x^6+13*x^5+9*x^4+41*x^3+x^2+2*x+27", "y^2=52*x^6+52*x^5+25*x^4+43*x^3+6*x^2+47*x+6", "y^2=33*x^6+58*x^5+7*x^4+14*x^3+17*x^2+28*x+54", "y^2=58*x^6+53*x^5+19*x^4+27*x^3+x^2+53*x+17", "y^2=29*x^6+30*x^5+7*x^4+x^3+12*x^2+21*x", "y^2=25*x^6+41*x^5+16*x^4+41*x^3+54*x^2+3*x+53", "y^2=48*x^6+5*x^5+19*x^4+9*x^3+19*x^2+8*x", "y^2=58*x^6+41*x^5+38*x^4+32*x^3+5*x^2+44*x+26", "y^2=29*x^6+54*x^5+33*x^4+51*x^3+35*x^2+x+15", "y^2=35*x^6+19*x^5+15*x^4+37*x^3+7*x^2+26*x+21"], "hyp_count": 24, "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_index": 9, "zfv_index_factorization": [[3, 2]], "zfv_plus_index": 3, "zfv_plus_index_factorization": [[3, 1]], "zfv_plus_norm": 4149, "geometric_splitting_field": "4.0.103725.1", "splitting_field": "4.0.103725.1", "geometric_splitting_polynomials": [[271, -14, 32, -1, 1]], "splitting_polynomials": [[271, -14, 32, -1, 1]], "is_squarefree": true, "is_geometrically_squarefree": true, "size": 30, "principal_polarization_count": 24, "pic_prime_gens": [[1, 11, 1, 6], [1, 19, 1, 3]]}