# Stored data for abelian variety isogeny class 2.53.a_dz, downloaded from the LMFDB on 05 September 2025.
{"abvar_count": 2913, "abvar_counts": [2913, 8485569, 22164585876, 62180968311081, 174887470674500793, 491268867054578687376, 1379946262056912572169057, 3876267913366479368627111049, 10888439761782910226760386367924, 30585627398924374856478739757628849], "abvar_counts_str": "2913 8485569 22164585876 62180968311081 174887470674500793 491268867054578687376 1379946262056912572169057 3876267913366479368627111049 10888439761782910226760386367924 30585627398924374856478739757628849 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.462044697230698, 0.537955302769302], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 54, "curve_counts": [54, 3016, 148878, 7880500, 418195494, 22164810622, 1174711139838, 62259672153124, 3299763591802134, 174887470983488536], "curve_counts_str": "54 3016 148878 7880500 418195494 22164810622 1174711139838 62259672153124 3299763591802134 174887470983488536 ", "curves": ["y^2=x^6+x^3+35", "y^2=32*x^6+39*x^5+18*x^4+3*x^3+52*x+49", "y^2=11*x^6+25*x^5+36*x^4+6*x^3+51*x+45", "y^2=14*x^6+11*x^5+3*x^4+15*x^3+19*x^2+16*x+43", "y^2=28*x^6+22*x^5+6*x^4+30*x^3+38*x^2+32*x+33", "y^2=9*x^6+16*x^5+19*x^4+23*x^3+32*x^2+37*x+10", "y^2=18*x^6+32*x^5+38*x^4+46*x^3+11*x^2+21*x+20", "y^2=34*x^6+32*x^5+18*x^4+40*x^3+45*x^2+13*x+36", "y^2=15*x^6+11*x^5+36*x^4+27*x^3+37*x^2+26*x+19", "y^2=41*x^6+33*x^5+3*x^4+36*x^3+36*x^2+52*x+42", "y^2=29*x^6+13*x^5+6*x^4+19*x^3+19*x^2+51*x+31", "y^2=47*x^6+13*x^5+45*x^4+33*x^3+29*x^2+42*x+34", "y^2=41*x^6+26*x^5+37*x^4+13*x^3+5*x^2+31*x+15", "y^2=49*x^6+47*x^5+38*x^4+43*x^3+33*x^2+10*x+3", "y^2=45*x^6+41*x^5+23*x^4+33*x^3+13*x^2+20*x+6", "y^2=29*x^6+14*x^5+10*x^4+15*x^3+6*x^2+48*x+50", "y^2=5*x^6+28*x^5+20*x^4+30*x^3+12*x^2+43*x+47", "y^2=19*x^6+11*x^5+48*x^4+15*x^3+4*x^2+22*x+15", "y^2=38*x^6+22*x^5+43*x^4+30*x^3+8*x^2+44*x+30", "y^2=43*x^6+13*x^5+5*x^4+x^3+6*x^2+35*x+13", "y^2=33*x^6+26*x^5+10*x^4+2*x^3+12*x^2+17*x+26", "y^2=29*x^6+30*x^5+5*x^4+21*x^3+19*x^2+x+36", "y^2=5*x^6+7*x^5+10*x^4+42*x^3+38*x^2+2*x+19", "y^2=48*x^6+28*x^5+22*x^3+21*x^2+6*x+43", "y^2=43*x^6+3*x^5+44*x^3+42*x^2+12*x+33", "y^2=39*x^6+14*x^5+5*x^4+39*x^3+36*x^2+49*x+19", "y^2=25*x^6+28*x^5+10*x^4+25*x^3+19*x^2+45*x+38", "y^2=52*x^6+5*x^5+28*x^4+5*x^3+4*x^2+31*x+37", "y^2=51*x^6+10*x^5+3*x^4+10*x^3+8*x^2+9*x+21", "y^2=52*x^6+40*x^5+27*x^4+23*x^3+41*x^2+46*x+41", "y^2=51*x^6+27*x^5+x^4+46*x^3+29*x^2+39*x+29", "y^2=42*x^6+16*x^5+47*x^4+39*x^3+48*x^2+9*x+41", "y^2=31*x^6+32*x^5+41*x^4+25*x^3+43*x^2+18*x+29", "y^2=x^6+x^3+19", "y^2=44*x^6+45*x^5+41*x^4+2*x^3+45*x^2+28*x+52", "y^2=35*x^6+37*x^5+29*x^4+4*x^3+37*x^2+3*x+51", "y^2=40*x^6+29*x^5+13*x^4+39*x^3+48*x^2+35*x+9", "y^2=27*x^6+5*x^5+26*x^4+25*x^3+43*x^2+17*x+18"], "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": 1, "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": ["2.0.627.1"], "geometric_splitting_field": "2.0.627.1", "geometric_splitting_polynomials": [[157, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 38, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 38, "label": "2.53.a_dz", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["4.0.6290064.6"], "p": 53, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 3, 1, 20], [1, 11, 1, 2]], "poly": [1, 0, 103, 0, 2809], "poly_str": "1 0 103 0 2809 ", "primitive_models": [], "principal_polarization_count": 40, "q": 53, "real_poly": [1, 0, -3], "simple_distinct": ["2.53.a_dz"], "simple_factors": ["2.53.a_dzA"], "simple_multiplicities": [1], "singular_primes": [], "size": 40, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.6290064.6", "splitting_polynomials": [[2809, 0, 103, 0, 1]], "twist_count": 4, "twists": [["2.53.a_adz", "2.7890481.aoty_dlbdwd", 4], ["2.53.ad_ce", "2.491258904256726154641.aboaqibwe_pvkhlqlpchdqrog", 12], ["2.53.d_ce", "2.491258904256726154641.aboaqibwe_pvkhlqlpchdqrog", 12]], "weak_equivalence_count": 1, "zfv_index": 1, "zfv_index_factorization": [], "zfv_is_bass": true, "zfv_is_maximal": true, "zfv_pic_size": 40, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 43681, "zfv_singular_count": 0, "zfv_singular_primes": []}