# Stored data for abelian variety isogeny class 2.61.as_gg, downloaded from the LMFDB on 12 May 2026.
{"abvar_count": 2768, "abvar_counts": [2768, 13840000, 51434646608, 191545600000000, 713273575365721808, 2654348974340866960000, 9876838433491911353353808, 36751691388489819033600000000, 136753050146317599574069362749648, 508858109619679131335161212826000000], "abvar_counts_str": "2768 13840000 51434646608 191545600000000 713273575365721808 2654348974340866960000 9876838433491911353353808 36751691388489819033600000000 136753050146317599574069362749648 508858109619679131335161212826000000 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.0531652068084335, 0.446834793191567], "center_dim": 4, "cohen_macaulay_max": 2, "curve_count": 44, "curve_counts": [44, 3722, 226604, 13834158, 844514204, 51520374362, 3142744713404, 191707300122718, 11694145862442764, 713342911662882602], "curve_counts_str": "44 3722 226604 13834158 844514204 51520374362 3142744713404 191707300122718 11694145862442764 713342911662882602 ", "curves": ["y^2=52*x^6+12*x^5+12*x^4+33*x^3+49*x^2+32", "y^2=47*x^6+43*x^5+20*x^4+55*x^3+46*x^2+15*x+38", "y^2=31*x^6+51*x^5+58*x^4+52*x^3+2*x^2+9*x", "y^2=19*x^6+33*x^5+50*x^4+23*x^3+35*x^2+48*x+13", "y^2=8*x^6+43*x^5+56*x^4+36*x^3+9*x^2+39*x+35", "y^2=7*x^6+4*x^5+48*x^4+48*x^3+53*x^2+6*x+8", "y^2=57*x^6+59*x^5+45*x^4+7*x^3+13*x^2+20*x+18", "y^2=29*x^6+9*x^5+19*x^4+30*x^3+7*x^2+31*x+39", "y^2=26*x^6+x^5+4*x^4+x^3+34*x^2+7*x+18", "y^2=4*x^6+10*x^5+13*x^4+13*x^3+54*x^2+31*x+11", "y^2=55*x^6+38*x^5+27*x^4+57*x^3+25*x^2+7", "y^2=8*x^6+57*x^5+25*x^4+46*x^3+16*x^2+26", "y^2=19*x^6+26*x^5+31*x^4+34*x^3+3*x^2+24*x+29", "y^2=46*x^6+46*x^5+31*x^4+3*x^3+45*x^2+24*x+8", "y^2=18*x^6+50*x^5+25*x^4+47*x^3+38*x^2+30", "y^2=8*x^6+36*x^5+14*x^4+10*x^3+51*x+55", "y^2=2*x^6+57*x^5+57*x^4+60*x^3+19*x^2+14*x+55", "y^2=26*x^6+21*x^5+57*x^4+38*x^3+50*x^2+53*x+26", "y^2=44*x^6+6*x^5+18*x^4+44*x^3+55*x^2+16*x+59", "y^2=9*x^6+46*x^5+28*x^4+46*x^3+10*x^2+43*x+39", "y^2=28*x^6+6*x^5+5*x^4+17*x^3+50*x^2+x+14", "y^2=36*x^6+43*x^5+21*x^4+41*x^3+3*x^2+6*x+54", "y^2=55*x^6+45*x^5+56*x^4+11*x^3+4*x^2+2*x+2", "y^2=6*x^6+50*x^5+59*x^4+27*x^3+5*x^2+21*x+33", "y^2=48*x^6+13*x^5+28*x^4+3*x^3+42*x^2+27*x+51", "y^2=4*x^6+17*x^5+6*x^4+33*x^3+28*x^2+4*x+59", "y^2=41*x^6+54*x^5+41*x^4+15*x^2+29*x+19", "y^2=13*x^6+44*x^5+51*x^4+39*x^3+32*x^2+55", "y^2=x^6+50*x^5+46*x^4+33*x^3+40*x^2+36*x+1", "y^2=59*x^6+48*x^5+38*x^4+31*x^3+59*x^2+37*x+29", "y^2=44*x^6+48*x^5+40*x^4+8*x^3+53*x^2+7*x+7", "y^2=26*x^6+43*x^5+49*x^4+27*x^3+57*x^2+32*x+31", "y^2=31*x^6+39*x^5+37*x^4+35*x^3+4*x^2+48*x+26", "y^2=59*x^6+44*x^5+12*x^4+38*x^3+55*x^2+14*x+47", "y^2=57*x^6+45*x^5+40*x^4+14*x^3+30*x^2+29*x+52", "y^2=34*x^6+52*x^5+10*x^4+19*x^3+19*x^2+59*x+57", "y^2=21*x^6+57*x^5+22*x^4+28*x^3+40*x^2+10*x+22", "y^2=19*x^6+20*x^5+56*x^4+12*x^3+24*x^2+45*x+28", "y^2=56*x^6+36*x^5+20*x^4+59*x^3+8*x^2+42*x+59", "y^2=44*x^6+46*x^5+8*x^4+21*x^3+39*x^2+57*x+10", "y^2=53*x^5+16*x^4+16*x^2+8*x", "y^2=9*x^6+25*x^5+24*x^4+24*x^2+36*x+9", "y^2=55*x^6+33*x^5+8*x^4+38*x^3+35*x^2+24*x+60", "y^2=50*x^5+16*x^4+16*x^2+11*x", "y^2=8*x^5+28*x^4+19*x^3+54*x^2+24*x+19", "y^2=53*x^6+3*x^5+23*x^4+26*x^3+15*x^2+49*x+31", "y^2=60*x^6+5*x^5+x^4+54*x^3+34*x^2+32*x+26", "y^2=2*x^6+39*x^5+56*x^4+52*x^3+20*x^2+4*x+56", "y^2=8*x^6+18*x^5+22*x^4+58*x^3+21*x^2+19*x+54", "y^2=13*x^6+8*x^5+8*x^4+50*x^3+60*x^2+57*x+26", "y^2=54*x^6+18*x^5+5*x^4+5*x^3+50*x^2+17*x+56", "y^2=37*x^6+10*x^5+29*x^4+37*x^3+51*x^2+59", "y^2=10*x^6+18*x^5+16*x^4+22*x^3+20*x^2+57*x+18", "y^2=21*x^5+8*x^4+8*x^2+40*x", "y^2=43*x^5+55*x^4+52*x^3+3*x^2+10*x+60", "y^2=12*x^6+31*x^5+12*x^4+53*x^3+22*x^2+51*x+51", "y^2=21*x^6+57*x^5+32*x^4+44*x^3+47*x^2+20*x+31", "y^2=21*x^6+27*x^5+7*x^4+40*x^3+36*x^2+4*x+38", "y^2=29*x^6+59*x^5+7*x^4+40*x^3+37*x^2+57*x+53", "y^2=48*x^6+52*x^5+3*x^4+46*x^3+14*x^2+22*x+48", "y^2=41*x^6+40*x^5+58*x^4+7*x^3+16*x^2+38*x+52", "y^2=39*x^6+24*x^5+41*x^4+52*x^3+53*x^2+17*x+12", "y^2=30*x^6+43*x^5+22*x^4+34*x^3+10*x^2+10*x+20", "y^2=21*x^6+x^5+9*x^4+8*x^3+30*x^2+27*x+35", "y^2=47*x^6+23*x^5+16*x^4+46*x^3+8*x^2+13*x+54", "y^2=12*x^6+48*x^5+23*x^4+11*x^3+44*x^2+49*x+5", "y^2=17*x^6+31*x^5+58*x^4+22*x^3+22*x^2+57*x+39", "y^2=25*x^6+7*x^5+10*x^4+10*x^3+24*x^2+3*x+32", "y^2=31*x^6+9*x^5+8*x^4+28*x^3+53*x^2+35*x+14", "y^2=31*x^6+18*x^5+16*x^3+51*x^2+57*x+8", "y^2=52*x^6+53*x^5+60*x^4+30*x^3+19*x^2+53*x+14", "y^2=28*x^6+26*x^5+54*x^4+45*x^3+13*x^2+29*x+22"], "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": 10, "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": 4, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.164.1"], "geometric_splitting_field": "2.0.164.1", "geometric_splitting_polynomials": [[41, 0, 1]], "group_structure_count": 4, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 72, "is_cyclic": false, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 72, "label": "2.61.as_gg", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 8, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.26896.1"], "p": 61, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 5, 1, 8], [1, 3, 1, 8]], "poly": [1, -18, 162, -1098, 3721], "poly_str": "1 -18 162 -1098 3721 ", "primitive_models": [], "principal_polarization_count": 72, "q": 61, "real_poly": [1, -18, 40], "simple_distinct": ["2.61.as_gg"], "simple_factors": ["2.61.as_ggA"], "simple_multiplicities": [1], "singular_primes": ["2,5*F+2*V-35", "5,-5*F^2+4*F-1"], "size": 124, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.26896.1", "splitting_polynomials": [[100, 0, 21, 0, 1]], "twist_count": 4, "twists": [["2.61.s_gg", "2.3721.a_aiqs", 2], ["2.61.a_abo", "2.191707312997281.abcenfo_dagmikjmmxq", 8], ["2.61.a_bo", "2.191707312997281.abcenfo_dagmikjmmxq", 8]], "weak_equivalence_count": 12, "zfv_index": 40, "zfv_index_factorization": [[2, 3], [5, 1]], "zfv_is_bass": false, "zfv_is_maximal": false, "zfv_pic_size": 32, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 1600, "zfv_singular_count": 4, "zfv_singular_primes": ["2,5*F+2*V-35", "5,-5*F^2+4*F-1"]}