Database - hmf_fields

Formats: - HTML - YAML - JSON - 2026-10-23T22:38:46.994082

Query: /api/hmf_fields/?_offset=0

Table hmf_fields

Information on base fields for Hilbert modular forms

Column	Type	Example
degree	smallint	2
discriminant	bigint	296
ideals	jsonb	['[1, 1, 1]', '[2, 2, w]', '[4, 2, 2]', '[5, 5, w + 2]', '[5, 5, w + 3]', '[7, 7, w + 9]', '[7, 7, -...
label	text	'2.2.296.1'
narrow_class_no	smallint	2
primes	jsonb	['[2, 2, w]', '[5, 5, w + 2]', '[5, 5, w + 3]', '[7, 7, w + 9]', '[7, 7, -w + 9]', '[9, 3, 3]', '[13...

{'degree': 3, 'discriminant': 169, 'id': 3, 'ideals': ['[1, 1, 1]', '[5, 5, -w^2 + 2*w + 3]', '[5, 5, -w^2 + w + 2]', '[5, 5, -w + 1]', '[8, 2, 2]', '[13, 13, -w^2 + 3]', '[25, 5, -w^2 + 4]', '[25, 5, -w^2 + 3*w + 3]', '[25, 5, -2*w^2 + 3*w + 4]', '[25, 25, -2*w^2 + 4*w + 5]', '[25, 25, -2*w^2 + 2*w + 5]', '[25, 25, -2*w + 1]', '[27, 3, 3]', '[31, 31, -2*w^2 + 3*w + 3]', '[31, 31, -w^2 + 5]', '[31, 31, -w^2 + 3*w + 4]', '[40, 10, -2*w^2 + 4*w + 6]', '[40, 10, -2*w^2 + 2*w + 4]', '[40, 10, -2*w + 2]', '[47, 47, 2*w - 3]', '[47, 47, 2*w^2 - 4*w - 7]', '[47, 47, 2*w^2 - 2*w - 3]', '[53, 53, 3*w^2 - 4*w - 8]', '[53, 53, 4*w^2 - 6*w - 11]', '[53, 53, 3*w^2 - 5*w - 6]', '[64, 4, 4]', '[65, 65, w + 4]', '[65, 65, w^2 - 2*w + 2]', '[65, 65, -w^2 + w + 7]', '[73, 73, w^2 - 4*w - 4]', '[73, 73, 2*w^2 - w - 8]', '[73, 73, 3*w^2 - 5*w - 5]', '[79, 79, -3*w^2 + 5*w + 4]', '[79, 79, 2*w^2 - w - 9]', '[79, 79, w^2 - 4*w - 5]', '[83, 83, w^2 + w - 4]', '[83, 83, 3*w^2 - 4*w - 7]', '[83, 83, -2*w^2 + 5*w + 5]', '[103, 103, 3*w^2 - 6*w - 8]', '[103, 103, 3*w - 2]', '[103, 103, 3*w^2 - 3*w - 7]', '[104, 26, -2*w^2 + 6]', '[109, 109, 3*w^2 - 4*w - 6]', '[109, 109, 2*w^2 - 5*w - 6]', '[109, 109, w^2 + w - 5]', '[125, 5, 5]', '[125, 25, -4*w^2 + 5*w + 11]', '[125, 25, -w^2 - w + 7]', '[125, 25, -2*w^2 + 5*w + 8]', '[125, 25, -w^2 - 2*w + 3]', '[125, 25, -3*w^2 + 7*w + 6]', '[125, 25, -3*w^2 + 4*w + 4]', '[125, 125, -w^2 - w + 6]', '[125, 125, -3*w^2 + 4*w + 5]', '[125, 125, -2*w^2 + 5*w + 7]', '[131, 131, -4*w^2 + 8*w + 9]', '[131, 131, 4*w^2 - 4*w - 11]', '[131, 131, 4*w - 1]', '[135, 15, -3*w^2 + 6*w + 9]', '[135, 15, -3*w^2 + 3*w + 6]', '[135, 15, -3*w + 3]', '[151, 151, -w^2 + 3*w - 4]', '[151, 151, -w^2 - 3]', '[151, 151, 2*w^2 - 3*w - 11]', '[155, 155, -2*w^2 + 7]', '[155, 155, -w^2 + 2*w + 8]', '[155, 155, -4*w^2 + 6*w + 9]', '[155, 155, -2*w^2 + 6*w + 5]', '[155, 155, -3*w^2 + 3*w + 5]', '[155, 155, -3*w + 4]', '[155, 155, -3*w^2 + 6*w + 10]', '[155, 155, w^2 - w + 3]', '[155, 155, -w + 6]', '[157, 157, 4*w^2 - 7*w - 13]', '[157, 157, 3*w^2 - 6*w - 11]', '[157, 157, 3*w^2 - 2*w - 5]', '[169, 13, w^2 - 5*w + 3]', '[181, 181, w^2 + 2*w - 4]', '[181, 181, 4*w^2 - 5*w - 10]', '[181, 181, -3*w^2 + 7*w + 7]', '[200, 10, -2*w^2 + 8]', '[200, 10, -2*w^2 + 6*w + 6]', '[200, 10, -4*w^2 + 6*w + 8]', '[200, 50, -4*w^2 + 8*w + 10]', '[200, 50, -4*w^2 + 4*w + 10]', '[200, 50, -4*w + 2]', '[216, 6, 6]', '[229, 229, -w - 6]', '[229, 229, -w^2 + 2*w - 4]', '[229, 229, w^2 - w - 9]', '[233, 233, 2*w^2 - 6*w - 7]', '[233, 233, 4*w^2 - 6*w - 7]', '[233, 233, 2*w^2 - 9]', '[235, 235, 5*w^2 - 8*w - 11]', '[235, 235, 3*w^2 - w - 10]', '[235, 235, -w^2 - w - 4]', '[235, 235, -2*w^2 + 5*w - 3]', '[235, 235, 3*w^2 - 4*w - 15]', '[235, 235, w^2 + 2*w - 5]', '[235, 235, 3*w^2 - 7*w - 8]', '[235, 235, 4*w^2 - 5*w - 9]', '[235, 235, 2*w^2 - 7*w - 5]', '[239, 239, w^2 - 10]', '[239, 239, -w^2 + 3*w + 9]', '[239, 239, 2*w^2 - 11]', '[248, 62, -4*w^2 + 6*w + 6]', '[248, 62, -2*w^2 + 10]', '[248, 62, -2*w^2 + 6*w + 8]', '[265, 265, 6*w^2 - 11*w - 15]', '[265, 265, 2*w^2 - 3*w - 12]', '[265, 265, 5*w^2 - 4*w - 23]', '[265, 265, 5*w^2 - 11*w - 9]', '[265, 265, w^2 + 2*w - 10]', '[265, 265, 4*w^2 - 8*w - 11]', '[265, 265, 3*w^2 - 3*w - 16]', '[265, 265, 4*w^2 - 3*w - 17]', '[265, 265, w - 7]', '[281, 281, 3*w^2 - 7*w - 9]', '[281, 281, w^2 + 2*w - 6]', '[281, 281, 4*w^2 - 5*w - 8]', '[307, 307, 3*w^2 - w - 11]', '[307, 307, 2*w^2 - 7*w - 6]', '[307, 307, 5*w^2 - 8*w - 10]', '[311, 311, -4*w^2 + 3*w + 8]', '[311, 311, 5*w^2 - 9*w - 15]', '[311, 311, 3*w^2 - 7*w - 12]', '[313, 313, 3*w^2 - 7*w - 10]', '[313, 313, w^2 + 2*w - 7]', '[313, 313, 4*w^2 - 5*w - 7]', '[317, 317, 5*w^2 - 7*w - 12]', '[317, 317, -3*w^2 + 8*w + 7]', '[317, 317, 2*w^2 + w - 7]', '[320, 20, -4*w^2 + 8*w + 12]', '[320, 20, -4*w^2 + 4*w + 8]', '[320, 20, -4*w + 4]', '[325, 65, -4*w^2 + 5*w + 6]', '[325, 65, -3*w^2 + 7*w + 11]', '[325, 65, -w^2 - 2*w + 8]', '[325, 325, -w^2 - 3*w + 4]', '[325, 325, -4*w^2 + 9*w + 9]', '[325, 325, -5*w^2 + 6*w + 13]', '[337, 337, 2*w^2 - 2*w - 13]', '[337, 337, -2*w^2 + 4*w - 3]', '[337, 337, -2*w - 7]', '[343, 7, -7]', '[351, 39, -3*w^2 + 9]', '[359, 359, 4*w^2 - 4*w - 7]', '[359, 359, 4*w - 5]', '[359, 359, 4*w^2 - 8*w - 13]', '[365, 365, -w - 7]', '[365, 365, 7*w^2 - 9*w - 21]', '[365, 365, -w^2 + 2*w - 5]', '[365, 365, 2*w^2 + 3*w - 4]', '[365, 365, 4*w^2 - 8*w - 15]', '[365, 365, 5*w^2 - 12*w - 8]', '[365, 365, 4*w - 7]', '[365, 365, 4*w^2 - 4*w - 5]', '[365, 365, w^2 - w - 10]', '[376, 94, 4*w - 6]', '[376, 94, 4*w^2 - 8*w - 14]', '[376, 94, 4*w^2 - 4*w - 6]', '[389, 389, 6*w^2 - 7*w - 17]', '[389, 389, 3*w^2 - 4*w - 16]', '[389, 389, -5*w^2 + 11*w + 10]', '[395, 395, w^2 - 6*w + 4]', '[395, 395, 4*w^2 - 3*w - 6]', '[395, 395, 3*w^2 + 2*w - 6]', '[395, 395, w^2 - 11]', '[395, 395, w^2 - 3*w - 10]', '[395, 395, -5*w^2 + 13*w + 7]', '[395, 395, 5*w^2 - 9*w - 17]', '[395, 395, 2*w^2 - 3*w + 3]', '[395, 395, 8*w^2 - 11*w - 24]', '[403, 403, -5*w^2 + 8*w + 8]', '[403, 403, -3*w^2 + w + 13]', '[403, 403, -2*w^2 + 7*w + 8]', '[415, 415, 5*w^2 - 6*w - 12]', '[415, 415, w^2 - 2*w - 10]', '[415, 415, -w^2 - 3*w + 5]', '[415, 415, 2*w^2 - 7*w - 9]', '[415, 415, 4*w^2 - 9*w - 10]', '[415, 415, 3*w^2 - w - 14]', '[415, 415, -5*w^2 + 8*w + 7]', '[415, 415, -w^2 + w - 5]', '[415, 415, -w + 8]', '[421, 421, 2*w^2 - 3*w - 13]', '[421, 421, -w^2 + 3*w - 6]', '[421, 421, -w^2 - 5]', '[424, 106, 6*w^2 - 8*w - 16]', '[424, 106, 8*w^2 - 12*w - 22]', '[424, 106, 6*w^2 - 10*w - 12]', '[443, 443, 5*w^2 - 5*w - 12]', '[443, 443, 5*w - 3]', '[443, 443, -5*w^2 + 10*w + 13]', '[463, 463, 5*w^2 - 7*w - 10]', '[463, 463, 2*w^2 + w - 9]', '[463, 463, 3*w^2 - 8*w - 9]', '[467, 467, 3*w^2 - 10]', '[467, 467, -6*w^2 + 9*w + 14]', '[467, 467, 3*w^2 - 9*w - 7]', '[499, 499, 4*w^2 - 9*w - 11]', '[499, 499, w^2 + 3*w - 6]', '[499, 499, 5*w^2 - 6*w - 11]', '[512, 8, 8]', '[515, 515, 6*w^2 - 10*w - 11]', '[515, 515, 2*w^2 - 8*w - 7]', '[515, 515, w^2 - 4*w - 11]', '[515, 515, 2*w^2 - w - 15]', '[515, 515, -3*w^2 + 5*w - 2]', '[515, 515, 3*w^2 - 8*w - 10]', '[515, 515, 2*w^2 + w - 10]', '[515, 515, 5*w^2 - 7*w - 9]', '[515, 515, 4*w^2 - 2*w - 15]', '[520, 130, 2*w + 8]', '[520, 130, 2*w^2 - 4*w + 4]', '[520, 130, -2*w^2 + 2*w + 14]', '[521, 521, w^2 + 4*w - 4]', '[521, 521, -5*w^2 + 11*w + 11]', '[521, 521, 6*w^2 - 7*w - 16]', '[541, 541, w^2 + 3*w - 12]', '[541, 541, 5*w^2 - 6*w - 5]', '[541, 541, 4*w^2 - 9*w - 17]', '[545, 545, -w - 8]', '[545, 545, -w^2 + 2*w - 6]', '[545, 545, 2*w^2 + w - 11]', '[545, 545, 3*w^2 - 8*w - 11]', '[545, 545, 5*w^2 - 7*w - 8]', '[545, 545, 6*w^2 - 8*w - 15]', '[545, 545, 2*w^2 + 2*w - 7]', '[545, 545, 4*w^2 - 10*w - 9]', '[545, 545, w^2 - w - 11]', '[547, 547, w^2 + w - 13]', '[547, 547, -2*w^2 + 5*w + 14]', '[547, 547, 2*w^2 + w - 12]', '[571, 571, 5*w^2 - 6*w - 10]', '[571, 571, 4*w^2 - 9*w - 12]', '[571, 571, w^2 + 3*w - 7]', '[577, 577, 3*w^2 - 11]', '[577, 577, 3*w^2 - 9*w - 8]', '[577, 577, -6*w^2 + 9*w + 13]', '[584, 146, 2*w^2 - 8*w - 8]', '[584, 146, 4*w^2 - 2*w - 16]', '[584, 146, 6*w^2 - 10*w - 10]', '[593, 593, 6*w^2 - 13*w - 12]', '[593, 593, 7*w^2 - 8*w - 20]', '[593, 593, 3*w^2 - 4*w - 17]', '[599, 599, 6*w^2 - 5*w - 15]', '[599, 599, -w^2 + 8*w - 1]', '[599, 599, -7*w^2 + 13*w + 18]', '[611, 611, w^2 - 2*w - 11]', '[611, 611, 7*w^2 - 6*w - 19]', '[611, 611, w^2 - 8*w - 9]', '[619, 619, 6*w^2 - 11*w - 18]', '[619, 619, 4*w^2 - 9*w - 16]', '[619, 619, w^2 + 3*w - 11]', '[625, 25, -4*w^2 + 2*w + 17]', '[625, 25, -2*w^2 + 8*w + 9]', '[625, 25, -6*w^2 + 10*w + 9]', '[625, 25, -5*w^2 + 10*w + 15]', '[625, 25, -5*w^2 + 5*w + 10]', '[625, 25, -5*w + 5]', '[625, 125, w^2 - 3*w + 7]', '[625, 125, -7*w^2 + 10*w + 18]', '[625, 125, -3*w^2 - w + 9]', '[625, 125, -2*w^2 + 3*w + 14]', '[625, 125, w^2 + 6]', '[625, 125, -4*w^2 + 11*w + 8]', '[625, 625, -w^2 - 3*w + 8]', '[625, 625, -4*w^2 + 9*w + 13]', '[625, 625, -5*w^2 + 6*w + 9]', '[632, 158, -6*w^2 + 10*w + 8]', '[632, 158, 4*w^2 - 2*w - 18]', '[632, 158, 2*w^2 - 8*w - 10]', '[655, 655, -7*w^2 + 6*w + 25]', '[655, 655, w^2 - 9*w - 6]', '[655, 655, -3*w^2 + 7*w + 18]', '[655, 655, -4*w^2 + 5*w - 1]', '[655, 655, -w^2 - 2*w + 15]', '[655, 655, -4*w^2 + 9*w + 15]', '[655, 655, -w^2 - 3*w + 10]', '[655, 655, -8*w^2 + 15*w + 13]', '[655, 655, 5*w^2 - 6*w - 7]', '[664, 166, 2*w^2 + 2*w - 8]', '[664, 166, 6*w^2 - 8*w - 14]', '[664, 166, -4*w^2 + 10*w + 10]', '[675, 15, -3*w^2 + 12]', '[675, 15, -3*w^2 + 9*w + 9]', '[675, 15, -6*w^2 + 9*w + 12]', '[675, 75, -6*w^2 + 12*w + 15]', '[675, 75, -6*w^2 + 6*w + 15]', '[675, 75, -6*w + 3]', '[677, 677, 2*w^2 + 3*w - 6]', '[677, 677, -7*w^2 + 9*w + 19]', '[677, 677, 5*w^2 - 12*w - 10]', '[689, 689, 9*w^2 - 14*w - 31]', '[689, 689, 6*w^2 - 11*w - 23]', '[689, 689, 5*w^2 - 10*w - 16]', '[701, 701, 5*w^2 - 10*w - 19]', '[701, 701, 6*w^2 - 11*w - 19]', '[701, 701, 5*w^2 - 4*w - 9]', '[727, 727, 5*w^2 - 5*w - 8]', '[727, 727, 5*w - 7]', '[727, 727, 5*w^2 - 10*w - 17]', '[729, 9, 9]', '[733, 733, 5*w^2 - 3*w - 8]', '[733, 733, 5*w^2 - 10*w - 18]', '[733, 733, 7*w^2 - 12*w - 23]', '[755, 755, 3*w^2 - 9*w - 10]', '[755, 755, 7*w^2 - 14*w - 16]', '[755, 755, 5*w^2 - 2*w - 6]', '[755, 755, 8*w^2 - 13*w - 28]', '[755, 755, 6*w^2 - 9*w - 11]', '[755, 755, 7*w - 2]', '[755, 755, 7*w^2 - 7*w - 19]', '[755, 755, -3*w^2 + 11*w - 3]', '[755, 755, 3*w^2 - 13]', '[775, 155, -7*w^2 + 8*w + 19]', '[775, 155, -2*w^2 + w + 16]', '[775, 155, -4*w^2 + 10*w + 11]', '[775, 155, -w^2 - 5*w + 4]', '[775, 155, -6*w^2 + 8*w + 13]', '[775, 155, -w^2 + 4*w + 12]', '[775, 155, -6*w^2 + 13*w + 13]', '[775, 155, 3*w^2 - 5*w + 3]', '[775, 155, -2*w^2 - 2*w + 9]', '[775, 775, w + 9]', '[775, 775, w^2 - 2*w + 7]', '[775, 775, -6*w^2 + 11*w + 21]', '[775, 775, -7*w^2 + 11*w + 15]', '[775, 775, -4*w^2 + w + 14]', '[775, 775, w^2 - 7*w + 6]', '[775, 775, -w^2 + w + 12]', '[775, 775, -3*w^2 + 10*w + 8]', '[775, 775, -5*w^2 + 4*w + 7]', '[785, 785, 5*w^2 - 2*w - 16]', '[785, 785, -w^2 - 4*w - 8]', '[785, 785, 6*w^2 - 7*w - 28]', '[785, 785, 7*w^2 - 10*w - 17]', '[785, 785, 5*w^2 - 7*w - 24]', '[785, 785, 3*w^2 + w - 10]', '[785, 785, 6*w^2 - 7*w - 14]', '[785, 785, 2*w^2 - 9*w - 8]', '[785, 785, 5*w^2 - 3*w - 19]', '[811, 811, 3*w^2 - 14]', '[811, 811, 6*w^2 - 9*w - 10]', '[811, 811, 3*w^2 - 9*w - 11]', '[824, 206, 6*w^2 - 12*w - 16]', '[824, 206, 6*w - 4]', '[824, 206, 6*w^2 - 6*w - 14]', '[827, 827, -2*w^2 + 5*w + 15]', '[827, 827, 3*w^2 - 16]', '[827, 827, w^2 + w - 14]', '[832, 52, -4*w^2 + 12]', '[837, 93, -6*w^2 + 9*w + 9]', '[837, 93, -3*w^2 + 15]', '[837, 93, -3*w^2 + 9*w + 12]', '[845, 65, -2*w^2 - 3*w + 7]', '[845, 65, -5*w^2 + 12*w + 11]', '[845, 65, -7*w^2 + 9*w + 18]', '[853, 853, -2*w^2 + 5*w - 6]', '[853, 853, 3*w^2 - 4*w - 18]', '[853, 853, -w^2 - w - 7]', '[857, 857, -2*w^2 + 3*w - 5]', '[857, 857, w^2 - 13]', '[857, 857, w^2 - 3*w - 12]', '[859, 859, w^2 - 2*w - 12]', '[859, 859, -w^2 + w - 7]', '[859, 859, w - 10]', '[863, 863, 2*w^2 - 9*w - 9]', '[863, 863, 4*w^2 - 6*w - 21]', '[863, 863, 5*w^2 - 3*w - 20]', '[872, 218, 6*w^2 - 8*w - 12]', '[872, 218, 4*w^2 - 10*w - 12]', '[872, 218, 2*w^2 + 2*w - 10]', '[883, 883, -w^2 + 3*w - 8]', '[883, 883, -w^2 - 7]', '[883, 883, 2*w^2 - 3*w - 15]', '[905, 905, 2*w^2 - 9*w - 10]', '[905, 905, 5*w^2 - 3*w - 21]', '[905, 905, -2*w^2 + 2*w - 5]', '[905, 905, 2*w^2 - 4*w - 15]', '[905, 905, 5*w^2 - 11*w - 14]', '[905, 905, -2*w + 11]', '[905, 905, -w^2 - 4*w + 7]', '[905, 905, 6*w^2 - 7*w - 13]', '[905, 905, -7*w^2 + 12*w + 10]', '[911, 911, 4*w^2 - w - 15]', '[911, 911, 3*w^2 - 10*w - 9]', '[911, 911, 7*w^2 - 11*w - 14]', '[937, 937, 7*w^2 - 13*w - 20]', '[937, 937, 4*w^2 - 10*w - 17]', '[937, 937, 2*w^2 + 2*w - 15]', '[941, 941, -7*w^2 + 10*w + 16]', '[941, 941, 4*w^2 - 11*w - 10]', '[941, 941, 3*w^2 + w - 11]', '[949, 949, 4*w^2 - 10*w - 13]', '[949, 949, 6*w^2 - w - 9]', '[949, 949, 5*w^2 - 9*w - 25]', '[961, 31, -6*w^2 + 13*w + 14]', '[961, 31, -7*w^2 + 8*w + 18]', '[961, 31, -w^2 - 5*w + 5]', '[961, 961, -6*w^2 + 6*w + 13]', '[961, 961, -6*w^2 + 12*w + 17]', '[961, 961, -6*w + 5]', '[967, 967, 3*w^2 - 3*w - 19]', '[967, 967, -7*w^2 + 14*w + 17]', '[967, 967, 7*w^2 - 7*w - 18]', '[983, 983, 8*w^2 - 11*w - 21]', '[983, 983, -5*w^2 + 13*w + 10]', '[983, 983, -8*w^2 + 13*w + 17]', '[1000, 10, 10]', '[1000, 50, -8*w^2 + 10*w + 22]', '[1000, 50, -2*w^2 - 2*w + 14]', '[1000, 50, -4*w^2 + 10*w + 16]', '[1000, 50, -2*w^2 - 4*w + 6]', '[1000, 50, -6*w^2 + 14*w + 12]', '[1000, 50, -6*w^2 + 8*w + 8]', '[1000, 250, -2*w^2 - 2*w + 12]', '[1000, 250, -6*w^2 + 8*w + 10]', '[1000, 250, -4*w^2 + 10*w + 14]', '[1009, 1009, 5*w^2 - 11*w - 15]', '[1009, 1009, w^2 + 4*w - 8]', '[1009, 1009, 6*w^2 - 7*w - 12]', '[1013, 1013, 7*w^2 - 9*w - 17]', '[1013, 1013, -5*w^2 + 12*w + 12]', '[1013, 1013, 2*w^2 + 3*w - 8]', '[1019, 1019, -4*w^2 + 5*w - 2]', '[1019, 1019, w^2 + 2*w - 16]', '[1019, 1019, -3*w^2 + 7*w + 19]', '[1027, 1027, -3*w^2 + 10*w + 10]', '[1027, 1027, 6*w^2 - 9*w - 28]', '[1027, 1027, 7*w^2 - w - 12]', '[1039, 1039, -4*w^2 + 13*w + 8]', '[1039, 1039, -5*w^2 + 14*w + 9]', '[1039, 1039, 9*w^2 - 13*w - 24]', '[1048, 262, -8*w^2 + 16*w + 18]', '[1048, 262, 8*w^2 - 8*w - 22]', '[1048, 262, 8*w - 2]', '[1061, 1061, -w - 10]', '[1061, 1061, -w^2 + 2*w - 8]', '[1061, 1061, w^2 - w - 13]', '[1079, 1079, -6*w^2 + 5*w + 12]', '[1079, 1079, w^2 - 6*w - 14]', '[1079, 1079, 5*w^2 - 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