# Stored data for abelian variety isogeny class 2.59.al_ck, downloaded from the LMFDB on 11 July 2026.
{"abvar_count": 2884, "abvar_counts": [2884, 12124336, 41928295696, 146746221813184, 511145450543334124, 1779200058995001723136, 6193381176163942376167804, 21559180947083363464396072704, 75047499080084539796283500590096, 261240335597249447748402647072777776], "abvar_counts_str": "2884 12124336 41928295696 146746221813184 511145450543334124 1779200058995001723136 6193381176163942376167804 21559180947083363464396072704 75047499080084539796283500590096 261240335597249447748402647072777776 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 1, "angle_rank": 1, "angles": [0.0873800814724294, 0.579286585194237], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 49, "curve_counts": [49, 3485, 204148, 12110409, 714964439, 42180596246, 2488649460941, 146830461713809, 8662996110245932, 511116753481932125], "curve_counts_str": "49 3485 204148 12110409 714964439 42180596246 2488649460941 146830461713809 8662996110245932 511116753481932125 ", "curves": ["y^2=33*x^6+20*x^5+x^4+30*x^3+53*x^2+42*x+28", "y^2=42*x^6+29*x^5+49*x^4+16*x^3+20*x^2+12*x+36", "y^2=56*x^6+34*x^5+18*x^4+4*x^3+6*x^2+39*x+10", "y^2=16*x^6+x^5+25*x^4+58*x^3+44*x^2+39*x+8", "y^2=50*x^6+28*x^5+3*x^4+35*x^3+19*x^2+15*x+32", "y^2=40*x^6+24*x^5+42*x^4+18*x^3+30*x^2+38*x+13", "y^2=36*x^6+27*x^5+23*x^4+13*x^3+21*x^2+18*x+51", "y^2=51*x^6+19*x^5+36*x^4+11*x^3+32*x^2+46*x+34", "y^2=31*x^6+8*x^5+56*x^4+x^3+51*x^2+53*x+33", "y^2=26*x^6+8*x^5+11*x^4+54*x^3+12*x^2+27*x+6", "y^2=52*x^6+52*x^5+6*x^4+31*x^3+37*x^2+53*x+23", "y^2=49*x^6+42*x^5+17*x^4+45*x^3+19*x^2+57*x+18", "y^2=26*x^6+54*x^5+53*x^4+6*x^3+18*x^2+29*x+30", "y^2=34*x^6+24*x^5+26*x^4+11*x^3+49*x^2+4*x+54", "y^2=6*x^6+34*x^5+11*x^4+17*x^3+7*x^2+36*x+18", "y^2=57*x^6+11*x^5+58*x^4+48*x^3+48*x^2+35*x+41", "y^2=9*x^6+35*x^5+16*x^4+41*x^3+55*x^2+13*x+14", "y^2=43*x^6+57*x^5+3*x^4+33*x^3+43*x^2+15*x+47", "y^2=49*x^6+51*x^5+8*x^4+31*x^3+31*x^2+33*x+21", "y^2=27*x^6+39*x^5+39*x^4+58*x^3+21*x+40", "y^2=52*x^6+52*x^5+20*x^4+42*x^3+55*x^2+37*x+50", "y^2=55*x^6+58*x^5+24*x^4+54*x^3+53*x^2+48*x+39", "y^2=7*x^6+6*x^5+28*x^4+47*x^3+26*x^2+53*x+7", "y^2=17*x^6+12*x^5+44*x^4+4*x^3+10*x^2+26*x+29", "y^2=32*x^6+5*x^4+20*x^3+8*x^2+38*x+2", "y^2=15*x^6+38*x^5+38*x^4+42*x^3+4*x^2+43*x+50", "y^2=14*x^6+29*x^5+23*x^4+2*x^3+x^2+55*x+21", "y^2=17*x^6+2*x^5+10*x^4+4*x^3+16*x^2+50*x+11", "y^2=54*x^6+x^5+37*x^4+20*x^3+12*x^2+26*x+43", "y^2=20*x^6+56*x^5+34*x^4+28*x^3+10*x^2+57*x+32", "y^2=46*x^6+23*x^5+49*x^4+48*x^3+26*x^2+22*x+12", "y^2=44*x^6+48*x^5+23*x^4+12*x^3+33*x^2+36*x+15", "y^2=4*x^6+38*x^5+28*x^4+38*x^3+2*x^2+26*x+9", "y^2=19*x^6+54*x^5+36*x^4+17*x^3+20*x^2+33*x+52", "y^2=35*x^6+4*x^5+45*x^4+47*x^3+28*x^2+2", "y^2=41*x^6+x^5+35*x^4+2*x^3+34*x^2+56*x+55", "y^2=42*x^6+20*x^5+57*x^4+48*x^3+11*x^2+28*x+4", "y^2=38*x^6+57*x^5+11*x^4+4*x^3+50*x^2+8*x+38", "y^2=43*x^6+49*x^5+9*x^4+50*x^3+43*x^2+52*x+9", "y^2=15*x^6+30*x^5+26*x^4+23*x^3+13*x^2+51*x+37", "y^2=38*x^6+28*x^5+2*x^4+19*x^3+9*x^2+44*x+44", "y^2=40*x^6+14*x^5+14*x^4+36*x^3+50*x^2+53*x+32", "y^2=49*x^6+28*x^5+x^4+48*x^3+14*x^2+58*x+40", "y^2=14*x^6+39*x^5+17*x^4+16*x^3+49*x^2+30*x+10", "y^2=54*x^6+41*x^5+52*x^4+7*x^3+54*x^2+42*x+56", "y^2=41*x^6+21*x^5+41*x^4+37*x^3+58*x^2+3*x+21", "y^2=9*x^6+35*x^5+28*x^4+4*x^3+13*x^2+25*x+50", "y^2=25*x^6+18*x^5+17*x^4+21*x^3+17*x^2+10*x+37", "y^2=36*x^6+3*x^5+54*x^4+38*x^3+55*x^2+x", "y^2=22*x^6+13*x^5+56*x^4+31*x^3+20*x^2+39*x+53", "y^2=7*x^6+47*x^5+35*x^4+11*x^3+44*x^2+42*x+22", "y^2=32*x^6+58*x^5+4*x^4+15*x^3+47*x^2+15*x", "y^2=3*x^6+39*x^5+43*x^4+45*x^3+41*x^2+40*x+42", "y^2=42*x^6+55*x^5+45*x^4+28*x^3+51*x^2+35*x+18", "y^2=11*x^6+47*x^5+21*x^4+43*x^3+55*x^2+6*x+57", "y^2=22*x^6+47*x^5+8*x^4+x^3+21*x^2+52*x+33", "y^2=28*x^6+4*x^5+20*x^4+56*x^3+44*x^2+39*x", "y^2=39*x^5+44*x^4+9*x^3+17*x^2+3*x+11", "y^2=19*x^6+33*x^5+58*x^4+49*x^3+36*x^2+52*x+8", "y^2=14*x^6+22*x^5+41*x^4+12*x^2+57*x+44", "y^2=10*x^6+x^5+37*x^4+57*x^3+22*x^2+42*x+16", "y^2=4*x^6+15*x^5+57*x^4+28*x^3+39*x^2+53*x+52"], "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": 4, "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": 3, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.115.1"], "geometric_splitting_field": "2.0.115.1", "geometric_splitting_polynomials": [[29, -1, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 62, "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": 62, "label": "2.59.al_ck", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 12, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.119025.3"], "p": 59, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 2, 1, 2], [1, 7, 1, 60]], "poly": [1, -11, 62, -649, 3481], "poly_str": "1 -11 62 -649 3481 ", "primitive_models": [], "principal_polarization_count": 62, "q": 59, "real_poly": [1, -11, -56], "simple_distinct": ["2.59.al_ck"], "simple_factors": ["2.59.al_ckA"], "simple_multiplicities": [1], "singular_primes": ["2,-8*F-7*V+77", "31,-F^2-8*F+6*V-74"], "size": 84, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.119025.3", "splitting_polynomials": [[841, -29, -28, -1, 1]], "twist_count": 6, "twists": [["2.59.l_ck", "2.3481.d_afdo", 2], ["2.59.w_jf", "2.205379.abvk_bsyyw", 3], ["2.59.aw_jf", "2.42180533641.dopw_kqgtizac", 6], ["2.59.a_ad", "2.42180533641.dopw_kqgtizac", 6], ["2.59.l_ck", "2.42180533641.dopw_kqgtizac", 6], ["2.59.a_d", "2.1779197418239532716881.utvqeoxo_ggygzayexiwxxobm", 12]], "weak_equivalence_count": 4, "zfv_index": 62, "zfv_index_factorization": [[2, 1], [31, 1]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 60, "zfv_plus_index": 1, "zfv_plus_index_factorization": [], "zfv_plus_norm": 3844, "zfv_singular_count": 4, "zfv_singular_primes": ["2,-8*F-7*V+77", "31,-F^2-8*F+6*V-74"]}