# Stored data for abelian variety isogeny class 2.41.a_f, downloaded from the LMFDB on 04 April 2026.
{"abvar_count": 1687, "abvar_counts": [1687, 2845969, 4750079152, 8003801151801, 13422659379748927, 22563251950265039104, 37929227194754213541727, 63758943335288602986755625, 107178930967532126102341260592, 180167784824761849683033557651329], "abvar_counts_str": "1687 2845969 4750079152 8003801151801 13422659379748927 22563251950265039104 37929227194754213541727 63758943335288602986755625 107178930967532126102341260592 180167784824761849683033557651329 ", "angle_corank": 1, "angle_rank": 1, "angles": [0.259710593423305, 0.740289406576695], "center_dim": 4, "cohen_macaulay_max": 1, "curve_count": 42, "curve_counts": [42, 1692, 68922, 2832436, 115856202, 4750054062, 194754273882, 7984914261028, 327381934393962, 13422659449345452], "curve_counts_str": "42 1692 68922 2832436 115856202 4750054062 194754273882 7984914261028 327381934393962 13422659449345452 ", "curves": ["y^2=28*x^6+27*x^5+6*x^4+35*x^3+38*x^2+18*x+16", "y^2=28*x^6+4*x^4+33*x^3+x^2+10*x+2", "y^2=4*x^6+24*x^4+34*x^3+6*x^2+19*x+12", "y^2=23*x^6+10*x^5+29*x^4+14*x^3+37*x^2+34*x+31", "y^2=15*x^6+19*x^5+10*x^4+2*x^3+17*x^2+40*x+22", "y^2=36*x^6+28*x^5+10*x^4+6*x^3+12*x^2+8*x+32", "y^2=11*x^6+4*x^5+19*x^4+36*x^3+31*x^2+7*x+28", "y^2=23*x^6+36*x^5+8*x^4+31*x^3+8*x^2+35", "y^2=15*x^6+11*x^5+7*x^4+22*x^3+7*x^2+5", "y^2=28*x^6+40*x^5+36*x^4+3*x^3+x^2+x+21", "y^2=4*x^6+35*x^5+11*x^4+18*x^3+6*x^2+6*x+3", "y^2=35*x^6+27*x^5+21*x^4+15*x^3+22*x^2+26*x+5", "y^2=5*x^6+39*x^5+3*x^4+8*x^3+9*x^2+33*x+30", "y^2=2*x^6+13*x^5+35*x^4+21*x^3+x^2+10*x+20", "y^2=12*x^6+37*x^5+5*x^4+3*x^3+6*x^2+19*x+38", "y^2=33*x^6+11*x^5+19*x^4+17*x^3+31*x^2+31*x+35", "y^2=34*x^6+25*x^5+32*x^4+20*x^3+22*x^2+22*x+5", "y^2=34*x^6+34*x^5+24*x^4+40*x^3+22*x^2+21*x+7", "y^2=33*x^6+7*x^5+28*x^4+19*x^3+6*x^2+28*x+35", "y^2=34*x^6+x^5+4*x^4+32*x^3+36*x^2+4*x+5", "y^2=7*x^6+x^5+3*x^4+20*x^3+21*x^2+31*x+4", "y^2=x^6+6*x^5+18*x^4+38*x^3+3*x^2+22*x+24", "y^2=39*x^6+21*x^5+34*x^4+30*x^3+18*x^2+28*x+12", "y^2=29*x^6+3*x^5+40*x^4+16*x^3+26*x^2+4*x+31", "y^2=20*x^6+24*x^5+3*x^4+7*x^3+23*x^2+9*x+26", "y^2=38*x^6+21*x^5+18*x^4+x^3+15*x^2+13*x+33", "y^2=18*x^6+9*x^5+15*x^4+18*x^3+19*x^2+32*x+11", "y^2=25*x^6+30*x^5+18*x^4+24*x^3+28*x^2+37*x+7", "y^2=27*x^6+16*x^5+26*x^4+21*x^3+4*x^2+17*x+1", "y^2=15*x^6+9*x^5+30*x^4+17*x^3+16*x^2+13*x+36", "y^2=8*x^6+13*x^5+16*x^4+20*x^3+14*x^2+37*x+11", "y^2=10*x^6+23*x^5+38*x^4+14*x^3+26*x^2+2*x+31", "y^2=19*x^6+15*x^5+23*x^4+2*x^3+33*x^2+12*x+22", "y^2=40*x^6+25*x^5+2*x^4+34*x^3+21*x^2+13*x+25", "y^2=26*x^6+6*x^5+32*x^4+29*x^3+23*x^2+8*x+1", "y^2=23*x^6+x^5+24*x^4+31*x^3+5*x^2+18*x+14", "y^2=15*x^6+6*x^5+21*x^4+22*x^3+30*x^2+26*x+2", "y^2=14*x^6+7*x^5+7*x^4+3*x^3+21*x^2+40*x+37", "y^2=2*x^6+x^5+x^4+18*x^3+3*x^2+35*x+17", "y^2=22*x^6+24*x^5+9*x^4+28*x^3+11*x^2+30*x+15", "y^2=9*x^6+21*x^5+13*x^4+4*x^3+25*x^2+16*x+8", "y^2=34*x^6+17*x^5+40*x^4+17*x^3+28*x^2+30*x+29", "y^2=40*x^6+20*x^5+35*x^4+20*x^3+4*x^2+16*x+10", "y^2=28*x^6+28*x^5+38*x^4+24*x^2+17*x+28", "y^2=4*x^6+4*x^5+23*x^4+21*x^2+20*x+4", "y^2=38*x^6+7*x^5+15*x^4+18*x^3+31*x^2+6*x+40", "y^2=23*x^6+x^5+8*x^4+26*x^3+22*x^2+36*x+35", "y^2=10*x^6+37*x^5+10*x^4+19*x^3+38*x^2+16*x+38", "y^2=19*x^6+17*x^5+19*x^4+32*x^3+23*x^2+14*x+23", "y^2=13*x^6+26*x^5+14*x^4+19*x^3+9*x^2+16*x+39", "y^2=37*x^6+33*x^5+2*x^4+32*x^3+13*x^2+14*x+29", "y^2=17*x^6+38*x^5+24*x^4+2*x^3+6*x^2+19*x+26", "y^2=20*x^6+23*x^5+21*x^4+12*x^3+36*x^2+32*x+33", "y^2=4*x^6+13*x^5+38*x^4+22*x^3+19*x^2+9*x+36", "y^2=24*x^6+37*x^5+23*x^4+9*x^3+32*x^2+13*x+11", "y^2=34*x^6+10*x^5+11*x^4+29*x^3+40*x^2+40*x+26", "y^2=40*x^6+19*x^5+25*x^4+10*x^3+35*x^2+35*x+33", "y^2=36*x^6+22*x^5+34*x^4+22*x^3+39*x^2+32*x+23", "y^2=11*x^6+9*x^5+40*x^4+9*x^3+29*x^2+28*x+15", "y^2=3*x^6+20*x^5+16*x^4+29*x^3+22*x^2+x+33", "y^2=18*x^6+38*x^5+14*x^4+10*x^3+9*x^2+6*x+34", "y^2=19*x^6+22*x^5+8*x^4+x^3+32*x^2+25*x+34", "y^2=32*x^6+9*x^5+7*x^4+6*x^3+28*x^2+27*x+40", "y^2=28*x^6+18*x^5+13*x^4+24*x^3+27*x^2+24*x+1", "y^2=4*x^6+26*x^5+37*x^4+21*x^3+39*x^2+21*x+6", "y^2=37*x^6+10*x^5+21*x^4+21*x^3+5*x^2+2*x+2", "y^2=17*x^6+19*x^5+3*x^4+3*x^3+30*x^2+12*x+12", "y^2=21*x^6+35*x^5+34*x^4+11*x^3+34*x^2+15*x+38", "y^2=10*x^6+5*x^5+3*x^4+37*x^3+24*x^2+17*x+8", "y^2=19*x^6+30*x^5+18*x^4+17*x^3+21*x^2+20*x+7", "y^2=17*x^6+18*x^5+x^4+3*x^3+27*x^2+3*x+19", "y^2=20*x^6+26*x^5+6*x^4+18*x^3+39*x^2+18*x+32", "y^2=8*x^6+17*x^5+15*x^4+22*x^3+27*x^2+37*x+35", "y^2=7*x^6+20*x^5+8*x^4+9*x^3+39*x^2+17*x+5", "y^2=39*x^6+3*x^5+20*x^4+19*x^3+19*x^2+18*x+24", "y^2=29*x^6+18*x^5+38*x^4+32*x^3+32*x^2+26*x+21", "y^2=18*x^6+38*x^5+22*x^4+24*x^3+10*x^2+10*x+37", "y^2=26*x^6+23*x^5+9*x^4+21*x^3+19*x^2+19*x+17", "y^2=12*x^6+14*x^5+27*x^4+40*x^3+9*x^2+38*x+7", "y^2=31*x^6+2*x^5+39*x^4+35*x^3+13*x^2+23*x+1", "y^2=2*x^6+33*x^5+10*x^4+10*x^3+24*x^2+4*x+2", "y^2=12*x^6+34*x^5+19*x^4+19*x^3+21*x^2+24*x+12", "y^2=22*x^6+16*x^5+11*x^4+29*x^3+38*x^2+22*x+34", "y^2=29*x^6+3*x^5+5*x^4+39*x^3+40*x^2+7*x+14", "y^2=10*x^6+18*x^5+30*x^4+29*x^3+35*x^2+x+2", "y^2=22*x^6+6*x^4+2*x^3+25*x^2+23*x+6", "y^2=20*x^6+36*x^5+34*x^4+27*x^3+9*x^2+26*x+7", "y^2=38*x^6+11*x^5+40*x^4+39*x^3+13*x^2+33*x+1", "y^2=19*x^6+36*x^5+16*x^4+23*x^3+23*x+26", "y^2=32*x^6+11*x^5+14*x^4+15*x^3+15*x+33", "y^2=12*x^6+17*x^5+18*x^4+3*x^3+20*x^2+13*x+1", "y^2=31*x^6+20*x^5+26*x^4+18*x^3+38*x^2+37*x+6", "y^2=10*x^6+19*x^5+8*x^4+40*x^3+20*x^2+18*x+15", "y^2=19*x^6+32*x^5+7*x^4+35*x^3+38*x^2+26*x+8", "y^2=40*x^6+5*x^5+37*x^4+37*x^3+27*x^2+15*x+20", "y^2=35*x^6+30*x^5+17*x^4+17*x^3+39*x^2+8*x+38", "y^2=8*x^6+8*x^5+35*x^4+8*x^3+16*x^2+7*x+32", "y^2=36*x^6+25*x^5+17*x^4+x^3+x^2+4*x+33", "y^2=11*x^6+27*x^5+20*x^4+6*x^3+6*x^2+24*x+34", "y^2=10*x^6+17*x^5+24*x^4+11*x^3+11*x^2+17*x+18", "y^2=19*x^6+20*x^5+21*x^4+25*x^3+25*x^2+20*x+26", "y^2=5*x^6+17*x^5+40*x^4+11*x^3+32*x^2+17*x+26", "y^2=30*x^6+20*x^5+35*x^4+25*x^3+28*x^2+20*x+33", "y^2=22*x^6+19*x^5+25*x^4+37*x^3+34*x^2+30*x+7", "y^2=9*x^6+32*x^5+27*x^4+17*x^3+40*x^2+16*x+1", "y^2=23*x^6+x^5+21*x^4+8*x^3+20*x^2+29*x+10", "y^2=15*x^6+6*x^5+3*x^4+7*x^3+38*x^2+10*x+19", "y^2=9*x^6+11*x^5+23*x^4+27*x^3+2*x^2+28*x+25", "y^2=13*x^6+25*x^5+15*x^4+39*x^3+12*x^2+4*x+27", "y^2=16*x^6+7*x^5+13*x^3+5*x^2+13*x+24", "y^2=14*x^6+x^5+37*x^3+30*x^2+37*x+21", "y^2=16*x^6+9*x^5+16*x^4+6*x^3+28*x^2+26*x+40", "y^2=14*x^6+13*x^5+14*x^4+36*x^3+4*x^2+33*x+35", "y^2=13*x^6+33*x^5+10*x^4+18*x^3+18*x^2+9*x+27", "y^2=37*x^6+34*x^5+19*x^4+26*x^3+26*x^2+13*x+39", "y^2=3*x^6+39*x^5+28*x^4+38*x^3+29*x^2+35*x+26", "y^2=24*x^6+40*x^5+17*x^4+12*x^3+20*x^2+23*x+5", "y^2=21*x^6+35*x^5+20*x^4+31*x^3+38*x^2+15*x+30", "y^2=34*x^6+35*x^5+5*x^4+33*x^3+22*x^2+9*x+28", "y^2=40*x^6+5*x^5+30*x^4+34*x^3+9*x^2+13*x+4", "y^2=4*x^6+11*x^5+7*x^4+35*x^3+2*x^2+14*x+28", "y^2=24*x^6+25*x^5+x^4+5*x^3+12*x^2+2*x+4", "y^2=28*x^6+32*x^5+7*x^4+23*x^2+38*x+21", "y^2=4*x^6+28*x^5+x^4+15*x^2+23*x+3", "y^2=11*x^6+27*x^5+x^4+12*x^2+35*x+28", "y^2=29*x^6+28*x^5+34*x^4+7*x^3+23*x^2+35*x+34", "y^2=37*x^6+29*x^5+20*x^4+x^3+13*x^2+25*x+30", "y^2=17*x^6+10*x^5+38*x^4+6*x^3+37*x^2+27*x+16", "y^2=29*x^6+30*x^5+38*x^4+35*x^3+36*x^2+17*x+8", "y^2=10*x^6+16*x^5+23*x^4+5*x^3+11*x^2+20*x+7", "y^2=31*x^6+14*x^5+40*x^4+9*x^3+11*x^2+23*x+17", "y^2=22*x^6+2*x^5+35*x^4+13*x^3+25*x^2+15*x+20"], "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": 2, "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": 2, "geometric_galois_groups": ["2T1"], "geometric_number_fields": ["2.0.6699.1"], "geometric_splitting_field": "2.0.6699.1", "geometric_splitting_polynomials": [[1675, -1, 1]], "group_structure_count": 1, "has_geom_ss_factor": false, "has_jacobian": 1, "has_principal_polarization": 1, "hyp_count": 132, "is_cyclic": true, "is_geometrically_simple": false, "is_geometrically_squarefree": false, "is_primitive": true, "is_simple": true, "is_squarefree": true, "is_supersingular": false, "jacobian_count": 132, "label": "2.41.a_f", "max_divalg_dim": 1, "max_geom_divalg_dim": 1, "max_twist_degree": 4, "newton_coelevation": 2, "newton_elevation": 0, "noncyclic_primes": [], "number_fields": ["4.0.44876601.2"], "p": 41, "p_rank": 2, "p_rank_deficit": 0, "poly": [1, 0, 5, 0, 1681], "poly_str": "1 0 5 0 1681 ", "primitive_models": [], "q": 41, "real_poly": [1, 0, -77], "simple_distinct": ["2.41.a_f"], "simple_factors": ["2.41.a_fA"], "simple_multiplicities": [1], "singular_primes": ["2,-F-17*V-5"], "slopes": ["0A", "0B", "1A", "1B"], "splitting_field": "4.0.44876601.2", "splitting_polynomials": [[1681, 0, 5, 0, 1]], "twist_count": 2, "twists": [["2.41.a_af", "2.2825761.jws_bktczj", 4]], "weak_equivalence_count": 2, "zfv_index": 4, "zfv_index_factorization": [[2, 2]], "zfv_is_bass": true, "zfv_is_maximal": false, "zfv_plus_index": 2, "zfv_plus_index_factorization": [[2, 1]], "zfv_plus_norm": 7569, "zfv_singular_count": 2, "zfv_singular_primes": ["2,-F-17*V-5"]}