# Stored data for abelian variety isogeny class 2.61.aq_he, downloaded from the LMFDB on 03 October 2025.
{"abvar_count": 2916, "abvar_counts": [2916, 14288400, 51953908356, 191820284006400, 713299927426289316, 2654302364946880880400, 9876819544993997025708996, 36751698097816430477706854400, 136753057858358162634808539418596, 508858111105703527015772321150250000], "abvar_counts_str": "2916 14288400 51953908356 191820284006400 713299927426289316 2654302364946880880400 9876819544993997025708996 36751698097816430477706854400 136753057858358162634808539418596 508858111105703527015772321150250000 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.328850104904971, 0.328850104904971], "center_dim": 2, "curve_count": 46, "curve_counts": [46, 3838, 228886, 13853998, 844545406, 51519469678, 3142738703206, 191707335120478, 11694146521921486, 713342913746066398], "curve_counts_str": "46 3838 228886 13853998 844545406 51519469678 3142738703206 191707335120478 11694146521921486 713342913746066398 ", "curves": ["y^2=50*x^6+2*x^5+24*x^4+30*x^3+24*x^2+2*x+50", "y^2=16*x^6+58*x^4+58*x^2+16", "y^2=52*x^6+50*x^5+6*x^4+47*x^3+60*x^2+50*x+49", "y^2=37*x^6+3*x^5+35*x^4+24*x^3+36*x^2+44*x+50", "y^2=7*x^6+42*x^5+51*x^4+55*x^3+26*x^2+57*x+18", "y^2=49*x^6+54*x^5+10*x^4+34*x^3+7*x^2+13*x+37", "y^2=52*x^6+25*x^5+40*x^4+26*x^3+7*x^2+57*x+41", "y^2=29*x^6+10*x^5+27*x^4+34*x^3+27*x^2+10*x+29", "y^2=27*x^6+x^5+9*x^4+35*x^3+9*x^2+x+27", "y^2=39*x^6+60*x^5+15*x^4+10*x^3+2*x^2+56*x+7", "y^2=x^6+16*x^3+9", "y^2=38*x^6+59*x^5+42*x^4+2*x^3+42*x^2+59*x+38", "y^2=x^6+x^3+20", "y^2=32*x^6+44*x^5+19*x^4+38*x^3+22*x^2+31*x+5", "y^2=60*x^6+24*x^5+9*x^4+3*x^3+9*x^2+24*x+60", "y^2=58*x^6+10*x^5+56*x^4+3*x^3+56*x^2+10*x+58", "y^2=9*x^6+3*x^5+46*x^4+4*x^3+46*x^2+3*x+9", "y^2=42*x^6+50*x^5+41*x^4+13*x^3+32*x^2+23*x+11", "y^2=11*x^6+15*x^5+47*x^4+30*x^3+55*x^2+60*x+45", "y^2=58*x^6+23*x^4+23*x^2+58", "y^2=38*x^6+45*x^5+29*x^4+3*x^3+29*x^2+45*x+38", "y^2=6*x^6+48*x^5+27*x^4+33*x^3+22*x^2+19*x+26", "y^2=7*x^6+12*x^5+5*x^4+42*x^3+39*x^2+5*x+29", "y^2=4*x^6+56*x^5+28*x^4+53*x^3+20*x^2+54*x+53", "y^2=27*x^6+53*x^5+47*x^4+2*x^3+47*x^2+53*x+27", "y^2=35*x^6+18*x^5+59*x^4+38*x^3+20*x^2+50*x+24", "y^2=31*x^5+60*x^4+2*x^3+4*x^2+8*x", "y^2=37*x^6+51*x^5+46*x^4+33*x^3+53*x^2+44*x+31", "y^2=12*x^6+19*x^5+44*x^4+21*x^3+13*x^2+20*x+21", "y^2=x^6+39*x^3+27", "y^2=28*x^6+48*x^5+12*x^4+23*x^3+16*x^2+34*x+21", "y^2=24*x^5+20*x^4+45*x^3+25*x^2+7*x", "y^2=38*x^6+51*x^5+28*x^4+40*x^3+47*x^2+23*x+56", "y^2=10*x^6+2*x^5+8*x^4+13*x^3+8*x^2+2*x+10", "y^2=11*x^6+46*x^5+47*x^4+15*x^3+49*x^2+45*x+24", "y^2=55*x^6+56*x^5+40*x^4+31*x^3+7*x^2+13*x+7", "y^2=17*x^6+14*x^5+14*x^4+2*x^3+47*x^2+14*x+44", "y^2=43*x^6+39*x^5+37*x^4+8*x^3+24*x^2+39*x+18", "y^2=50*x^6+24*x^5+38*x^4+11*x^3+51*x^2+40*x+19", "y^2=35*x^6+x^5+6*x^4+38*x^3+5*x^2+7*x+18", "y^2=35*x^6+24*x^4+24*x^2+35", "y^2=10*x^6+7*x^5+47*x^4+56*x^3+32*x^2+22*x+33", "y^2=x^6+36*x^3+52", "y^2=21*x^6+24*x^5+27*x^4+34*x^3+3*x^2+50*x+54", "y^2=32*x^6+39*x^5+27*x^4+13*x^3+27*x^2+39*x+32", "y^2=24*x^6+17*x^5+14*x^4+22*x^3+14*x^2+17*x+24", "y^2=3*x^6+20*x^5+47*x^4+17*x^3+12*x^2+x+60", "y^2=31*x^6+56*x^5+46*x^4+18*x^3+22*x^2+15*x+51", "y^2=11*x^6+4*x^5+20*x^4+9*x^3+20*x^2+4*x+11", "y^2=x^6+25*x^3+9", "y^2=49*x^6+45*x^5+57*x^4+8*x^3+31*x^2+40*x+24", "y^2=x^6+56*x^3+58", "y^2=60*x^6+21*x^5+13*x^4+2*x^3+4*x^2+5*x+4"], "dim1_distinct": 1, "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, "g": 2, "galois_groups": ["2T1"], "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": 1, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.20.1"], "geometric_splitting_field": "2.0.20.1", "geometric_splitting_polynomials": [[5, 0, 1]], "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 53, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": false, "is_squarefree": false, "is_supersingular": false, "jacobian_count": 53, "label": "2.61.aq_he", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 6, "newton_coelevation": 2, "newton_elevation": 0, "number_fields": ["2.0.20.1"], "p": 61, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, -16, 186, -976, 3721], "poly_str": "1 -16 186 -976 3721 ", "primitive_models": [], "q": 61, "real_poly": [1, -16, 64], "simple_distinct": ["1.61.ai"], "simple_factors": ["1.61.aiA", "1.61.aiB"], "simple_multiplicities": [2], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "2.0.20.1", "splitting_polynomials": [[5, 0, 1]], "twist_count": 6, "twists": [["2.61.a_cg", "2.3721.em_pzq", 2], ["2.61.q_he", "2.3721.em_pzq", 2], ["2.61.i_d", "2.226981.cvg_czkfy", 3], ["2.61.a_acg", "2.13845841.mbs_dszsti", 4], ["2.61.ai_d", "2.51520374361.abzmho_bmhxuyfhm", 6]]}