# Stored data for abelian variety isogeny class 2.37.a_az, downloaded from the LMFDB on 08 November 2025.
{"abvar_count": 1345, "abvar_counts": [1345, 1809025, 2565813460, 3520407875625, 4808584235335225, 6583398711517171600, 9012061296121518171265, 12337506881213969969375625, 16890053810563290349504350580, 23122482348314450525468125800625], "abvar_counts_str": "1345 1809025 2565813460 3520407875625 4808584235335225 6583398711517171600 9012061296121518171265 12337506881213969969375625 16890053810563290349504350580 23122482348314450525468125800625 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.19515222749844, 0.80484777250156], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 38, "curve_counts": [38, 1320, 50654, 1878388, 69343958, 2565900510, 94931877134, 3512478021028, 129961739795078, 4808584098252600], "curve_counts_str": "38 1320 50654 1878388 69343958 2565900510 94931877134 3512478021028 129961739795078 4808584098252600 ", "curves": ["y^2=12*x^6+26*x^5+27*x^4+36*x^3+23*x^2+26*x+22", "y^2=24*x^6+15*x^5+17*x^4+35*x^3+9*x^2+15*x+7", "y^2=x^6+18*x^5+20*x^4+5*x^3+21*x^2+16*x+16", "y^2=2*x^6+36*x^5+3*x^4+10*x^3+5*x^2+32*x+32", "y^2=31*x^6+34*x^5+9*x^4+35*x^3+21*x^2+20*x+25", "y^2=25*x^6+31*x^5+18*x^4+33*x^3+5*x^2+3*x+13", "y^2=11*x^6+32*x^5+16*x^4+24*x^3+5*x^2+27*x+15", "y^2=22*x^6+27*x^5+32*x^4+11*x^3+10*x^2+17*x+30", "y^2=2*x^6+7*x^5+6*x^4+34*x^3+36*x^2+30*x+25", "y^2=23*x^6+9*x^5+12*x^4+5*x^3+7*x^2+36*x+35", "y^2=9*x^6+18*x^5+24*x^4+10*x^3+14*x^2+35*x+33", "y^2=34*x^6+19*x^5+12*x^4+7*x^3+30*x^2+30*x+19", "y^2=31*x^6+x^5+24*x^4+14*x^3+23*x^2+23*x+1", "y^2=x^6+13*x^5+17*x^4+34*x^3+9*x^2+11*x+13", "y^2=2*x^6+26*x^5+34*x^4+31*x^3+18*x^2+22*x+26", "y^2=2*x^6+13*x^5+20*x^4+36*x^3+24*x^2+2*x+32", "y^2=4*x^6+26*x^5+3*x^4+35*x^3+11*x^2+4*x+27", "y^2=8*x^6+23*x^5+5*x^4+32*x^3+10*x^2+18*x+27", "y^2=21*x^6+3*x^5+21*x^4+7*x^3+31*x^2+x+35", "y^2=4*x^6+20*x^5+15*x^4+13*x^3+27*x^2+29*x+18", "y^2=8*x^6+3*x^5+30*x^4+26*x^3+17*x^2+21*x+36", "y^2=2*x^6+2*x^5+35*x^4+30*x^3+11*x^2+5*x+28", "y^2=3*x^6+20*x^5+13*x^4+x^2+33*x+28", "y^2=6*x^6+3*x^5+26*x^4+2*x^2+29*x+19", "y^2=26*x^6+x^5+9*x^4+32*x^3+28*x+17", "y^2=15*x^6+2*x^5+18*x^4+27*x^3+19*x+34", "y^2=28*x^6+12*x^5+13*x^4+5*x^3+13*x^2+29*x+35", "y^2=19*x^6+24*x^5+26*x^4+10*x^3+26*x^2+21*x+33", "y^2=7*x^6+5*x^5+18*x^4+10*x^3+11*x^2+15*x+19", "y^2=12*x^6+33*x^5+15*x^4+4*x^3+35*x^2+35*x+15", "y^2=24*x^6+29*x^5+30*x^4+8*x^3+33*x^2+33*x+30", "y^2=3*x^6+7*x^5+9*x^4+29*x^3+2*x^2+4*x+18", "y^2=24*x^6+29*x^5+34*x^4+21*x^3+20*x^2+18*x+5", "y^2=11*x^6+21*x^5+31*x^4+5*x^3+3*x^2+36*x+10", "y^2=10*x^6+6*x^5+31*x^4+34*x^3+17*x+5", "y^2=20*x^6+12*x^5+25*x^4+31*x^3+34*x+10", "y^2=21*x^6+28*x^5+24*x^4+14*x^3+10*x^2+30*x+7", "y^2=5*x^6+19*x^5+11*x^4+28*x^3+20*x^2+23*x+14", "y^2=36*x^6+28*x^5+33*x^4+16*x^3+24*x^2+25*x+17", "y^2=35*x^6+19*x^5+29*x^4+32*x^3+11*x^2+13*x+34", "y^2=27*x^6+23*x^5+5*x^4+34*x^3+x^2+33*x+32", "y^2=17*x^6+9*x^5+10*x^4+31*x^3+2*x^2+29*x+27", "y^2=9*x^6+25*x^5+34*x^4+36*x^3+5*x^2+2*x+16", "y^2=18*x^6+13*x^5+31*x^4+35*x^3+10*x^2+4*x+32", "y^2=5*x^6+5*x^5+33*x^4+3*x^3+13*x^2+27*x+24", "y^2=10*x^6+10*x^5+29*x^4+6*x^3+26*x^2+17*x+11", "y^2=2*x^6+x^5+2*x^4+3*x^3+x^2+x+34", "y^2=4*x^6+2*x^5+4*x^4+6*x^3+2*x^2+2*x+31", "y^2=x^6+2*x^5+22*x^4+10*x^3+x^2+16*x+18", "y^2=2*x^6+4*x^5+7*x^4+20*x^3+2*x^2+32*x+36", "y^2=3*x^6+16*x^5+14*x^4+21*x^3+12*x^2+32*x+14", "y^2=6*x^6+32*x^5+28*x^4+5*x^3+24*x^2+27*x+28", "y^2=3*x^6+7*x^5+12*x^4+10*x^3+27*x^2+24*x+27", "y^2=6*x^6+14*x^5+24*x^4+20*x^3+17*x^2+11*x+17", "y^2=25*x^6+14*x^5+12*x^4+10*x^3+32*x^2+11*x+26", "y^2=13*x^6+28*x^5+24*x^4+20*x^3+27*x^2+22*x+15", "y^2=14*x^6+10*x^5+21*x^4+30*x^3+22*x^2+12*x+5", "y^2=28*x^6+20*x^5+5*x^4+23*x^3+7*x^2+24*x+10", "y^2=6*x^6+4*x^5+5*x^4+28*x^3+22*x^2+24*x+16", "y^2=12*x^6+8*x^5+10*x^4+19*x^3+7*x^2+11*x+32", "y^2=11*x^6+23*x^5+33*x^4+31*x^3+21*x^2+16*x+27", "y^2=22*x^6+9*x^5+29*x^4+25*x^3+5*x^2+32*x+17", "y^2=23*x^6+36*x^5+8*x^4+26*x^3+12*x^2+33*x+4", "y^2=9*x^6+35*x^5+16*x^4+15*x^3+24*x^2+29*x+8", "y^2=17*x^6+9*x^5+19*x^4+29*x^3+x^2+36*x+25", "y^2=3*x^6+29*x^5+22*x^4+18*x^3+7*x^2+5*x+24", "y^2=22*x^6+16*x^5+14*x^4+35*x^3+3*x^2+3*x+25", "y^2=4*x^6+15*x^5+23*x^4+26*x^3+15*x^2+3*x+13", "y^2=8*x^6+30*x^5+9*x^4+15*x^3+30*x^2+6*x+26", "y^2=28*x^6+10*x^5+35*x^4+18*x^3+3*x^2+4*x+35", "y^2=17*x^6+32*x^5+12*x^4+11*x^3+20*x^2+36*x+5", "y^2=34*x^6+27*x^5+24*x^4+22*x^3+3*x^2+35*x+10", "y^2=12*x^6+20*x^5+32*x^4+x^3+8*x^2+6*x+24", "y^2=24*x^6+3*x^5+27*x^4+2*x^3+16*x^2+12*x+11", "y^2=24*x^6+29*x^5+7*x^4+22*x^3+13*x^2+23*x+4", "y^2=16*x^6+25*x^5+26*x^3+4*x^2+20*x+24", "y^2=32*x^6+13*x^5+15*x^3+8*x^2+3*x+11", "y^2=9*x^6+14*x^5+3*x^4+22*x^3+12*x^2+21*x+32", "y^2=18*x^6+28*x^5+6*x^4+7*x^3+24*x^2+5*x+27", "y^2=24*x^6+36*x^5+21*x^4+20*x^3+24*x^2+7*x+30", "y^2=6*x^6+14*x^5+4*x^4+7*x^3+26*x^2+13*x+7", "y^2=12*x^6+28*x^5+8*x^4+14*x^3+15*x^2+26*x+14", "y^2=22*x^6+29*x^5+7*x^4+36*x^3+8*x^2+7*x+13", "y^2=7*x^6+21*x^5+14*x^4+35*x^3+16*x^2+14*x+26"], "dim1_distinct": 0, "dim1_factors": 0, "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": 8, "g": 2, "galois_groups": ["4T2"], "geom_dim1_distinct": 1, "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": 2, "geometric_extension_degree": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.11.1"], "geometric_splitting_field": "2.0.11.1", "geometric_splitting_polynomials": [[3, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 84, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 84, "label": "2.37.a_az", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.1936.1"], "p": 37, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 2], [1, 5, 1, 8], [1, 5, 2, 8], [1, 5, 3, 8], [1, 53, 1, 8]], "poly": [1, 0, -25, 0, 1369], "poly_str": "1 0 -25 0 1369 ", "primitive_models": [], "principal_polarization_count": 99, "q": 37, "real_poly": [1, 0, -99], "simple_distinct": ["2.37.a_az"], "simple_factors": ["2.37.a_azA"], "simple_multiplicities": [1], "singular_primes": ["3,14*F-19*V", "7,5*F^2-F-7*V", "7,F^2-F-4*V+4"], "size": 185, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.1936.1", "splitting_polynomials": [[9, 0, -5, 0, 1]], "twist_count": 6, "twists": [["2.37.ao_et", "2.1874161.ggo_rzhod", 4], ["2.37.a_z", "2.1874161.ggo_rzhod", 4], ["2.37.o_et", "2.1874161.ggo_rzhod", 4], ["2.37.ah_m", "2.6582952005840035281.apvugncm_hsrndntfhzallm", 12], ["2.37.h_m", "2.6582952005840035281.apvugncm_hsrndntfhzallm", 12]], "weak_equivalence_count": 8, "zfv_index": 441, "zfv_index_factorization": [[3, 2], [7, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 128, "zfv_plus_index": 3, "zfv_plus_index_factorization": [[3, 1]], "zfv_plus_norm": 2401, "zfv_singular_count": 6, "zfv_singular_primes": ["3,14*F-19*V", "7,5*F^2-F-7*V", "7,F^2-F-4*V+4"]}