# Stored data for abelian variety isogeny class 2.61.h_fc, downloaded from the LMFDB on 05 October 2025.
{"abvar_count": 4288, "abvar_counts": [4288, 14664960, 51260535808, 191590369920000, 713421316712387008, 2654356994006669475840, 9876815363461562392589248, 36751695677464171986270720000, 136753055679896672922904327410688, 508858108763885473657505205482784000], "abvar_counts_str": "4288 14664960 51260535808 191590369920000 713421316712387008 2654356994006669475840 9876815363461562392589248 36751695677464171986270720000 136753055679896672922904327410688 508858108763885473657505205482784000 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.540867587810525, 0.603713893499568], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 69, "curve_counts": [69, 3937, 225834, 13837393, 844689129, 51520530022, 3142737372669, 191707322495233, 11694146335634994, 713342910463187977], "curve_counts_str": "69 3937 225834 13837393 844689129 51520530022 3142737372669 191707322495233 11694146335634994 713342910463187977 ", "curves": ["y^2=54*x^6+x^5+5*x^4+7*x^3+31*x^2+2*x+29", "y^2=55*x^6+7*x^5+31*x^4+51*x^3+10*x^2+28*x+55", "y^2=12*x^6+58*x^5+27*x^4+28*x^3+16*x^2+5*x+48", "y^2=4*x^6+8*x^5+15*x^4+47*x^3+59*x^2+27*x+59", "y^2=33*x^6+30*x^5+19*x^4+32*x^3+57*x^2+42*x+45", "y^2=20*x^6+47*x^5+19*x^4+30*x^3+56*x^2+x+19", "y^2=25*x^6+25*x^5+39*x^4+51*x^3+9*x^2+59*x+2", "y^2=3*x^6+22*x^5+28*x^4+21*x^3+13*x^2+60*x+10", "y^2=9*x^6+40*x^5+56*x^4+24*x^3+31*x^2+21*x+20", "y^2=60*x^6+56*x^5+11*x^4+34*x^3+39*x^2+54*x+27", "y^2=51*x^6+27*x^5+x^4+60*x^3+8*x^2+25*x+35", "y^2=43*x^6+45*x^5+9*x^4+50*x^3+42*x^2+25*x+39", "y^2=37*x^6+19*x^5+59*x^4+38*x^3+x^2+4*x+25", "y^2=57*x^6+10*x^5+36*x^4+45*x^3+57*x^2+39*x+29", "y^2=26*x^6+33*x^5+43*x^4+26*x^3+24*x^2+54*x+18", "y^2=11*x^6+18*x^5+2*x^4+44*x^3+59*x^2+46*x+34", "y^2=57*x^6+46*x^5+21*x^4+22*x^3+19*x^2+9*x+1", "y^2=10*x^6+12*x^5+13*x^4+40*x^3+37*x^2+44*x+36", "y^2=x^6+50*x^5+59*x^4+31*x^3+46*x^2+14*x+47", "y^2=31*x^6+33*x^5+38*x^4+42*x^3+46*x^2+35*x+20", "y^2=5*x^6+57*x^5+28*x^4+46*x^3+14*x^2+48*x+60", "y^2=x^6+60*x^5+3*x^4+6*x^3+42*x^2+48*x+22", "y^2=9*x^6+27*x^5+10*x^4+9*x^3+28*x^2+4*x+16", "y^2=16*x^6+58*x^5+20*x^4+13*x^3+28*x^2+55*x+29", "y^2=x^6+50*x^5+25*x^4+16*x^3+18*x^2+20*x+56", "y^2=10*x^6+33*x^5+26*x^4+41*x^3+39*x^2+56*x", "y^2=45*x^6+25*x^5+51*x^4+27*x^3+60*x^2+18*x+35", "y^2=18*x^5+58*x^4+46*x^3+9*x^2+27*x+4", "y^2=14*x^6+22*x^5+31*x^4+15*x^3+53*x^2+18*x+53", "y^2=59*x^6+44*x^5+60*x^4+60*x^3+12*x^2+41*x+42", "y^2=20*x^6+24*x^5+37*x^4+58*x^3+16*x^2+7*x+6", "y^2=41*x^6+54*x^5+53*x^4+9*x^3+59*x^2+12*x+34", "y^2=14*x^6+17*x^5+41*x^4+19*x^3+43*x^2+11*x+26", "y^2=6*x^6+43*x^5+19*x^4+15*x^3+19*x^2+24*x+44", "y^2=27*x^6+9*x^5+60*x^4+27*x^3+11*x^2+52*x+48", "y^2=38*x^6+6*x^5+27*x^4+58*x^3+19*x^2+20*x+60", "y^2=42*x^6+36*x^5+45*x^4+38*x^3+20*x^2+13*x+27", "y^2=56*x^6+38*x^5+34*x^4+15*x^3+14*x^2+3*x+20", "y^2=45*x^6+21*x^5+44*x^4+15*x^2+33*x+21", "y^2=43*x^6+17*x^5+7*x^4+6*x^3+34*x^2+33*x+1", "y^2=53*x^6+33*x^5+29*x^4+14*x^3+57*x^2+12", "y^2=46*x^6+38*x^5+38*x^4+48*x^3+56*x^2+40*x+39", "y^2=3*x^6+35*x^5+47*x^4+24*x^3+47*x^2+36*x+47", "y^2=2*x^6+34*x^5+2*x^4+27*x^3+3*x^2+2*x+20", "y^2=39*x^6+34*x^5+48*x^4+44*x^3+35*x^2+13*x+43", "y^2=7*x^6+36*x^5+11*x^4+21*x^3+46*x^2+45*x+2", "y^2=50*x^6+19*x^5+14*x^4+44*x^3+34*x^2+9*x+12", "y^2=54*x^6+45*x^5+44*x^4+41*x^3+60*x^2+36*x+25"], "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": 9, "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": ["2.0.15.1", "2.0.219.1"], "geometric_splitting_field": "4.0.1199025.2", "geometric_splitting_polynomials": [[1315, 145, -16, -1, 1]], "group_structure_count": 3, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 48, "is_geometrically_simple": false, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": false, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 48, "label": "2.61.h_fc", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.15.1", "2.0.219.1"], "p": 61, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 5, 1, 2], [2, 5, 1, 4], [2, 11, 1, 12], [1, 19, 1, 6]], "poly": [1, 7, 132, 427, 3721], "poly_str": "1 7 132 427 3721 ", "primitive_models": [], "principal_polarization_count": 80, "q": 61, "real_poly": [1, 7, 10], "simple_distinct": ["1.61.c", "1.61.f"], "simple_factors": ["1.61.cA", "1.61.fA"], "simple_multiplicities": [1, 1], "singular_primes": ["2,F+9", "3,8*F+V+3"], "size": 160, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.1199025.2", "splitting_polynomials": [[1315, 145, -16, -1, 1]], "twist_count": 4, "twists": [["2.61.ah_fc", "2.3721.ih_bbym", 2], ["2.61.ad_ei", "2.3721.ih_bbym", 2], ["2.61.d_ei", "2.3721.ih_bbym", 2]], "weak_equivalence_count": 9, "zfv_index": 36, "zfv_index_factorization": [[2, 2], [3, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 48, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 52560, "zfv_singular_count": 4, "zfv_singular_primes": ["2,F+9", "3,8*F+V+3"]}