# Stored data for abelian variety isogeny class 2.53.i_ek, downloaded from the LMFDB on 14 June 2026.
{"abvar_count": 3356, "abvar_counts": [3356, 8363152, 22023068732, 62234161439744, 174905206459261276, 491258297186799941008, 1379945593441422698495612, 3876268974446326533665472512, 10888439653213852827511096595612, 30585627416773984335618196261731472], "abvar_counts_str": "3356 8363152 22023068732 62234161439744 174905206459261276 491258297186799941008 1379945593441422698495612 3876268974446326533665472512 10888439653213852827511096595612 30585627416773984335618196261731472 ", "all_polarized_product": false, "all_unpolarized_product": false, "angle_corank": 0, "angle_rank": 2, "angles": [0.525640191098653, 0.655377756781446], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 62, "curve_counts": [62, 2974, 147926, 7887246, 418237902, 22164333742, 1174710570662, 62259689195934, 3299763558900062, 174887471085551934], "curve_counts_str": "62 2974 147926 7887246 418237902 22164333742 1174710570662 62259689195934 3299763558900062 174887471085551934 ", "curves": ["y^2=40*x^6+45*x^5+47*x^4+24*x^3+25*x^2+31*x+10", "y^2=20*x^6+16*x^5+29*x^4+41*x^3+35*x^2+28*x+6", "y^2=17*x^6+20*x^5+5*x^4+7*x^3+43*x^2+5*x+31", "y^2=7*x^6+2*x^5+26*x^3+32*x^2+17*x+47", "y^2=21*x^6+42*x^5+19*x^4+21*x^3+38*x^2+42*x+46", "y^2=21*x^6+32*x^5+9*x^4+14*x^3+28*x^2+21*x+47", "y^2=4*x^6+46*x^5+4*x^4+26*x^3+43*x^2+25*x+47", "y^2=38*x^6+32*x^5+19*x^4+43*x^3+25*x^2+51*x+1", "y^2=12*x^6+48*x^5+32*x^4+10*x^3+30*x^2+15*x+14", "y^2=9*x^6+3*x^5+33*x^4+36*x^3+45*x^2+16*x+46", "y^2=8*x^6+14*x^5+13*x^4+21*x^3+30*x^2+12*x", "y^2=x^6+33*x^5+18*x^4+11*x^3+31*x^2+11*x+39", "y^2=24*x^6+42*x^5+20*x^4+x^3+22*x^2+29*x+34", "y^2=30*x^6+43*x^5+33*x^4+36*x^3+40*x^2+50*x+14", "y^2=48*x^6+37*x^5+45*x^4+29*x^2+4*x+33", "y^2=19*x^6+38*x^5+16*x^4+25*x^3+8*x^2+17*x+30", "y^2=3*x^6+37*x^5+47*x^4+12*x^3+8*x^2+24*x+29", "y^2=32*x^6+32*x^5+41*x^4+4*x^3+43*x+17", "y^2=10*x^6+2*x^5+21*x^4+16*x^3+10*x^2+3*x+6", "y^2=34*x^5+36*x^4+27*x^3+51*x^2+12*x+45", "y^2=41*x^6+17*x^5+30*x^4+25*x^3+24*x^2+21*x+38", "y^2=42*x^6+32*x^5+50*x^4+18*x^3+22*x^2+47*x+50", "y^2=35*x^6+26*x^5+6*x^4+46*x^3+25*x^2+18*x+47", "y^2=9*x^6+45*x^5+33*x^4+2*x^3+23*x^2+28*x+52", "y^2=40*x^6+37*x^5+26*x^4+3*x^3+13*x^2+38*x+13", "y^2=39*x^6+42*x^5+28*x^4+32*x^3+21*x^2+41*x+16", "y^2=3*x^6+32*x^5+5*x^4+4*x^3+37*x^2+45*x+26", "y^2=49*x^6+6*x^5+14*x^4+12*x^3+18*x^2+24*x+25", "y^2=38*x^6+12*x^5+34*x^4+16*x^3+2*x^2+41*x+33", "y^2=16*x^6+2*x^5+28*x^4+41*x^3+52*x^2+36*x", "y^2=2*x^6+17*x^5+41*x^4+6*x^3+32*x^2+7*x+34", "y^2=42*x^6+13*x^5+x^4+47*x^3+22*x^2+24*x+37", "y^2=49*x^6+37*x^5+3*x^4+49*x^3+19*x^2+32*x+29", "y^2=4*x^6+31*x^5+48*x^4+28*x^3+37*x^2+8*x+49", "y^2=45*x^6+22*x^5+12*x^3+22*x^2+19*x+28", "y^2=31*x^6+40*x^5+26*x^4+23*x^3+49*x^2+16*x+52", "y^2=21*x^6+31*x^5+27*x^4+13*x^3+10*x^2+32*x+6", "y^2=46*x^6+52*x^5+39*x^4+49*x^3+37*x^2+29*x+11", "y^2=43*x^6+50*x^5+32*x^4+47*x^3+24*x^2+2*x+44", "y^2=47*x^6+48*x^5+27*x^4+23*x^3+10*x^2+27*x+2", "y^2=x^6+5*x^5+30*x^4+49*x^3+46*x^2+42*x+10", "y^2=35*x^6+33*x^5+13*x^4+52*x^3+2*x^2+43*x+23", "y^2=33*x^6+25*x^5+48*x^4+45*x^3+10*x^2+22*x+13", "y^2=38*x^6+45*x^5+30*x^4+50*x^3+42*x^2+26*x+21", "y^2=x^6+9*x^5+20*x^4+4*x^3+8*x^2+40*x+1", "y^2=15*x^6+49*x^5+44*x^4+28*x^3+14*x+27", "y^2=x^6+32*x^5+x^4+45*x^3+41*x^2+x", "y^2=28*x^6+19*x^5+19*x^4+52*x^3+18*x^2+13*x+20", "y^2=45*x^6+19*x^5+30*x^4+42*x^3+48*x^2+34*x+30", "y^2=28*x^6+17*x^5+23*x^4+42*x^3+48*x^2+10*x+13", "y^2=10*x^6+18*x^5+42*x^4+49*x^3+15*x^2+21*x+50", "y^2=3*x^6+49*x^5+18*x^4+51*x^3+13*x^2+47*x+8", "y^2=25*x^6+6*x^5+31*x^4+5*x^3+16*x^2+34*x+24", "y^2=15*x^6+47*x^5+46*x^4+45*x^3+32*x^2+49*x+2", "y^2=23*x^6+48*x^5+4*x^4+25*x^3+x^2+13*x+28", "y^2=12*x^6+11*x^5+6*x^4+34*x^3+40*x^2+37*x+7", "y^2=23*x^6+3*x^5+48*x^4+34*x^3+36*x^2+33*x+18", "y^2=19*x^6+41*x^5+5*x^4+31*x^3+32*x^2+3*x+44", "y^2=8*x^6+11*x^5+21*x^4+46*x^3+50*x^2+8*x+14", "y^2=31*x^6+8*x^5+24*x^4+3*x^3+22*x^2+6*x+49", "y^2=36*x^5+22*x^4+8*x^3+24*x^2+16*x+3", "y^2=5*x^6+47*x^5+41*x^4+9*x^3+27*x^2+32*x+4", "y^2=52*x^6+47*x^5+43*x^4+7*x^3+35*x^2+30*x+48", "y^2=18*x^6+36*x^5+2*x^4+24*x^3+25*x^2+25*x+42", "y^2=4*x^6+34*x^5+11*x^4+32*x^3+34*x^2+9*x+44", "y^2=13*x^6+22*x^5+24*x^4+35*x^3+15*x^2+9*x+33", "y^2=40*x^6+23*x^5+19*x^4+15*x^3+38*x^2+50*x+18", "y^2=18*x^6+33*x^5+25*x^4+38*x^3+5*x^2+41*x+11", "y^2=46*x^6+17*x^5+16*x^4+27*x^3+15*x^2+31*x+50", "y^2=29*x^6+17*x^5+10*x^4+25*x^3+24*x^2+5*x+37", "y^2=13*x^6+12*x^5+18*x^4+18*x^3+3*x^2+34*x+16", "y^2=41*x^6+38*x^5+25*x^4+25*x^3+31*x^2+8*x+40", "y^2=31*x^5+52*x^4+32*x^3+45*x^2+10*x+32", "y^2=48*x^6+43*x^5+39*x^4+43*x^3+36*x^2+21*x+41", "y^2=11*x^6+51*x^5+35*x^4+17*x^3+7*x^2+50*x+46", "y^2=12*x^6+33*x^5+21*x^4+x^3+45*x^2+31*x+41", "y^2=31*x^6+36*x^5+40*x^4+24*x^3+41*x^2+11", "y^2=11*x^6+10*x^5+28*x^4+4*x^3+15*x^2+9*x+29", "y^2=43*x^6+28*x^5+41*x^4+18*x^3+3*x^2+43*x+30", "y^2=49*x^6+15*x^5+40*x^4+5*x^3+3*x^2+6*x+3", "y^2=44*x^6+17*x^5+19*x^4+14*x^3+x^2+22*x+31", "y^2=3*x^6+7*x^5+45*x^4+3*x^3+2*x^2+18*x+28", "y^2=10*x^6+24*x^5+43*x^4+31*x^3+47*x^2+44*x+30", "y^2=4*x^6+31*x^5+43*x^4+32*x^3+3*x^2+40*x+47", "y^2=11*x^6+25*x^5+12*x^4+6*x^3+4*x^2+47*x+11", "y^2=27*x^6+47*x^5+17*x^4+11*x^3+26*x^2+28*x+6", "y^2=13*x^6+49*x^4+44*x^3+33*x^2+39*x+41", "y^2=48*x^6+12*x^5+35*x^4+2*x^3+7*x^2+37*x+5", "y^2=2*x^6+12*x^5+14*x^4+5*x^3+48*x^2+2*x", "y^2=28*x^6+38*x^5+9*x^4+40*x^3+18*x^2+45*x+49", "y^2=35*x^6+x^5+37*x^4+37*x^3+33*x^2+39*x+3", "y^2=23*x^6+25*x^5+7*x^4+18*x^3+45*x^2+17*x+34", "y^2=13*x^6+12*x^5+35*x^4+46*x^3+31*x^2+19*x+39", "y^2=11*x^6+14*x^5+25*x^4+15*x^3+35*x^2+35*x+18", "y^2=16*x^6+10*x^5+24*x^4+39*x^3+46*x^2+33*x+28", "y^2=42*x^6+2*x^5+22*x^4+49*x^3+6*x^2+48*x+21", "y^2=35*x^6+27*x^5+21*x^4+48*x^3+9*x^2+9*x+28", "y^2=20*x^6+8*x^5+44*x^4+17*x^3+32*x+10", "y^2=19*x^6+18*x^5+17*x^4+x^3+35*x^2+12*x+14", "y^2=5*x^6+6*x^5+49*x^4+7*x^3+2*x^2+23*x+9", "y^2=20*x^6+12*x^5+26*x^4+32*x^3+30*x^2+5*x+41", "y^2=2*x^6+13*x^5+49*x^4+44*x^3+17*x+7", "y^2=15*x^6+49*x^5+50*x^4+8*x^3+14*x^2+34*x+8", "y^2=9*x^6+7*x^5+11*x^4+17*x^3+17*x^2+43*x+51", "y^2=15*x^6+5*x^5+12*x^4+16*x^3+21*x^2+41*x+21", "y^2=27*x^6+12*x^5+41*x^4+20*x^3+45*x^2+38*x", "y^2=35*x^6+28*x^5+9*x^4+50*x^3+x^2+3*x+21", "y^2=31*x^6+47*x^5+34*x^4+50*x^3+48*x^2+50*x+25", "y^2=9*x^6+38*x^5+50*x^4+45*x^3+47*x^2+34*x+49", "y^2=30*x^6+14*x^5+9*x^4+27*x^3+52*x^2+14*x+47", "y^2=29*x^6+5*x^5+4*x^4+5*x^2+22*x+44", "y^2=5*x^6+24*x^5+6*x^4+7*x^3+45*x^2+4*x+8"], "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": 5, "g": 2, "galois_groups": ["4T3"], "geom_dim1_distinct": 0, "geom_dim1_factors": 0, "geom_dim2_distinct": 1, "geom_dim2_factors": 1, "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": ["4T3"], "geometric_number_fields": ["4.0.139328.2"], "geometric_splitting_field": "4.0.139328.2", "geometric_splitting_polynomials": [[142, -24, 25, -2, 1]], "group_structure_count": 2, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 112, "is_cyclic": false, "is_geometrically_simple": true, "is_geometrically_squarefree": true, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 112, "label": "2.53.i_ek", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 2, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [2], "number_fields": ["4.0.139328.2"], "p": 53, "p_rank": 2, "p_rank_deficit": 0, "pic_prime_gens": [[1, 7, 1, 14], [1, 7, 3, 2], [1, 23, 1, 14]], "poly": [1, 8, 114, 424, 2809], "poly_str": "1 8 114 424 2809 ", "primitive_models": [], "principal_polarization_count": 112, "q": 53, "real_poly": [1, 8, 8], "simple_distinct": ["2.53.i_ek"], "simple_factors": ["2.53.i_ekA"], "simple_multiplicities": [1], "singular_primes": ["2,F^2+2*F+V+6"], "size": 140, "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.139328.2", "splitting_polynomials": [[142, -24, 25, -2, 1]], "twist_count": 2, "twists": [["2.53.ai_ek", "2.2809.gi_rna", 2]], "weak_equivalence_count": 5, "zfv_index": 16, "zfv_index_factorization": [[2, 4]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_pic_size": 56, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 34832, "zfv_singular_count": 2, "zfv_singular_primes": ["2,F^2+2*F+V+6"]}