Database - hmf_fields

Formats: - HTML - YAML - JSON - 2026-10-23T22:39:24.759946

Query: /api/hmf_fields/?_offset=0

Table hmf_fields

Information on base fields for Hilbert modular forms

Column	Type	Example
degree	smallint	4
discriminant	bigint	12544
ideals	jsonb	['[1, 1, 1]', '[2, 2, 1/3*w^3 + w^2 - 2/3*w - 2]', '[4, 2, -1/3*w^3 + 5/3*w]', '[7, 7, 1/3*w^3 - 8/3...
label	text	'4.4.12544.1'
narrow_class_no	smallint	4
primes	jsonb	['[2, 2, 1/3*w^3 + w^2 - 2/3*w - 2]', '[7, 7, 1/3*w^3 - 8/3*w + 2]', '[7, 7, -w + 2]', '[9, 3, w]', ...

{'degree': 4, 'discriminant': 2225, 'id': 68, 'ideals': ['[1, 1, 1]', '[4, 2, -w]', '[4, 2, 1/2*w^3 - 1/2*w^2 - 5/2*w + 1]', '[16, 2, 2]', '[16, 4, -w^3 + w^2 + 4*w]', '[16, 4, -1/2*w^3 + 3/2*w^2 + 3/2*w - 2]', '[19, 19, 1/2*w^3 - 3/2*w^2 - 1/2*w + 4]', '[19, 19, 1/2*w^3 + 1/2*w^2 - 5/2*w - 1]', '[25, 5, w^3 - w^2 - 3*w + 1]', '[29, 29, -1/2*w^3 + 3/2*w^2 + 3/2*w - 1]', '[29, 29, -w^2 + 5]', '[31, 31, -w^3 + 2*w^2 + 3*w - 3]', '[31, 31, -1/2*w^3 - 1/2*w^2 + 3/2*w + 3]', '[41, 41, -1/2*w^3 - 1/2*w^2 + 5/2*w]', '[41, 41, -1/2*w^3 + 3/2*w^2 + 1/2*w - 5]', '[59, 59, w^3 - w^2 - 5*w + 1]', '[59, 59, 3/2*w^3 - 1/2*w^2 - 11/2*w - 1]', '[61, 61, 3/2*w^3 - 1/2*w^2 - 11/2*w - 2]', '[61, 61, -2*w^2 + w + 7]', '[64, 4, -2*w]', '[64, 4, w^3 - w^2 - 5*w + 2]', '[64, 8, 1/2*w^3 + 1/2*w^2 - 7/2*w]', '[64, 8, w^3 - 4*w]', '[71, 71, 1/2*w^3 - 3/2*w^2 - 5/2*w + 6]', '[71, 71, -1/2*w^3 + 5/2*w^2 - 1/2*w - 5]', '[71, 71, 1/2*w^3 + 3/2*w^2 - 7/2*w - 5]', '[71, 71, -w^3 + 3*w^2 + 2*w - 7]', '[76, 38, 1/2*w^3 + 3/2*w^2 - 5/2*w - 5]', '[76, 38, w^3 - 3*w^2 - 2*w + 6]', '[76, 38, w^3 - 2*w^2 - 3*w + 2]', '[76, 38, -1/2*w^3 - 1/2*w^2 + 3/2*w + 4]', '[81, 3, -3]', '[89, 89, -1/2*w^3 + 5/2*w^2 + 3/2*w - 6]', '[100, 10, 1/2*w^3 - 5/2*w^2 - 1/2*w + 7]', '[100, 10, -2*w^2 + w + 4]', '[101, 101, w^2 - 2*w - 5]', '[101, 101, -1/2*w^3 - 1/2*w^2 + 7/2*w - 1]', '[109, 109, w^3 - 2*w^2 - 3*w + 1]', '[109, 109, -5/2*w^3 + 7/2*w^2 + 17/2*w - 8]', '[109, 109, 1/2*w^3 + 1/2*w^2 - 3/2*w - 5]', '[109, 109, -2*w^3 + 2*w^2 + 8*w - 1]', '[116, 58, 2*w^2 - w - 6]', '[116, 58, w^3 - 5*w]', '[116, 58, -1/2*w^3 + 3/2*w^2 - 1/2*w - 4]', '[116, 58, -1/2*w^3 + 5/2*w^2 + 1/2*w - 5]', '[121, 11, 3/2*w^3 - 3/2*w^2 - 9/2*w + 1]', '[121, 11, -3/2*w^3 + 3/2*w^2 + 9/2*w - 2]', '[124, 62, -w^3 + 2*w^2 + w - 4]', '[124, 62, 1/2*w^3 - 1/2*w^2 - 5/2*w - 3]', '[124, 62, 3/2*w^3 - 1/2*w^2 - 13/2*w]', '[124, 62, w - 4]', '[131, 131, -1/2*w^3 - 3/2*w^2 + 11/2*w + 6]', '[131, 131, -1/2*w^3 - 1/2*w^2 + 9/2*w + 2]', '[131, 131, -1/2*w^3 - 1/2*w^2 + 9/2*w + 1]', '[131, 131, -3/2*w^3 + 3/2*w^2 + 13/2*w - 5]', '[149, 149, 5/2*w^3 - 5/2*w^2 - 17/2*w]', '[149, 149, -1/2*w^3 + 3/2*w^2 + 3/2*w + 1]', '[151, 151, 2*w^3 - 2*w^2 - 7*w + 3]', '[151, 151, 5/2*w^3 - 5/2*w^2 - 19/2*w + 1]', '[164, 82, w^2 + w - 5]', '[164, 82, 1/2*w^3 + 1/2*w^2 - 3/2*w + 2]', '[164, 82, 2*w^3 - 2*w^2 - 7*w + 2]', '[164, 82, -w^3 + 2*w^2 + 4*w - 2]', '[181, 181, -w^3 + w^2 + w - 3]', '[181, 181, 1/2*w^3 - 5/2*w^2 + 1/2*w + 8]', '[191, 191, 1/2*w^3 + 3/2*w^2 - 9/2*w - 8]', '[191, 191, 3/2*w^3 - 3/2*w^2 - 13/2*w - 1]', '[211, 211, -1/2*w^3 + 3/2*w^2 - 1/2*w - 5]', '[211, 211, -w^3 + 5*w - 1]', '[229, 229, -2*w^3 + 4*w^2 + 6*w - 7]', '[229, 229, 3/2*w^3 - 3/2*w^2 - 15/2*w + 4]', '[236, 118, w + 4]', '[236, 118, 1/2*w^3 - 5/2*w^2 - 1/2*w + 11]', '[236, 118, -1/2*w^3 - 5/2*w^2 + 7/2*w + 10]', '[236, 118, -w^3 - 2*w^2 + 4*w + 6]', '[239, 239, w^3 + w^2 - 4*w - 1]', '[239, 239, -3/2*w^3 + 1/2*w^2 + 15/2*w - 1]', '[241, 241, 1/2*w^3 + 1/2*w^2 - 1/2*w - 4]', '[241, 241, 3/2*w^3 - 5/2*w^2 - 11/2*w + 3]', '[244, 122, -w^3 - 2*w^2 + 6*w + 9]', '[244, 122, 2*w^3 - w^2 - 7*w]', '[244, 122, -w^3 - 2*w^2 + 5*w + 6]', '[244, 122, 7/2*w^3 - 7/2*w^2 - 27/2*w + 5]', '[256, 4, 4]', '[256, 8, -2*w^3 + 2*w^2 + 8*w]', '[256, 8, -w^3 + 3*w^2 + 3*w - 4]', '[256, 16, -w^3 + w^2 + 6*w - 4]', '[256, 16, -1/2*w^3 + 1/2*w^2 + 9/2*w + 1]', '[269, 269, -w^3 + 2*w^2 + w - 5]', '[269, 269, -3/2*w^3 + 5/2*w^2 + 7/2*w - 8]', '[269, 269, 3/2*w^3 - 7/2*w^2 - 7/2*w + 4]', '[269, 269, -w^3 - w^2 + 4*w + 7]', '[281, 281, -1/2*w^3 + 5/2*w^2 - 1/2*w - 9]', '[281, 281, 1/2*w^3 + 3/2*w^2 - 7/2*w - 1]', '[284, 142, 3*w^3 - 4*w^2 - 12*w + 11]', '[284, 142, -2*w^3 + w^2 + 6*w + 2]', '[284, 142, -5/2*w^3 + 7/2*w^2 + 15/2*w - 4]', '[284, 142, -5/2*w^3 + 3/2*w^2 + 19/2*w + 2]', '[284, 142, w^3 - 5*w + 2]', '[284, 142, -7/2*w^3 + 11/2*w^2 + 23/2*w - 11]', '[284, 142, -2*w^3 + 3*w^2 + 4*w - 2]', '[284, 142, -2*w^3 + 3*w^2 + 5*w - 4]', '[289, 17, -w^3 + 2*w^2 + 5*w - 1]', '[289, 17, -1/2*w^3 + 3/2*w^2 + 7/2*w - 7]', '[304, 38, w^3 - 3*w^2 - w + 8]', '[304, 38, w^3 + w^2 - 5*w - 2]', '[304, 76, -1/2*w^3 + 1/2*w^2 + 9/2*w - 3]', '[304, 76, w^3 - w^2 - 6*w]', '[304, 76, w^3 - 2*w^2 + 4]', '[304, 76, 2*w^3 - w^2 - 9*w + 1]', '[324, 6, 3*w]', '[324, 6, -3/2*w^3 + 3/2*w^2 + 15/2*w - 3]', '[331, 331, 3/2*w^3 - 3/2*w^2 - 15/2*w + 2]', '[331, 331, -5/2*w^3 + 7/2*w^2 + 17/2*w - 4]', '[331, 331, 3*w - 1]', '[331, 331, -3/2*w^3 + 1/2*w^2 + 7/2*w + 3]', '[349, 349, -1/2*w^3 - 1/2*w^2 + 5/2*w - 3]', '[349, 349, -1/2*w^3 + 3/2*w^2 + 1/2*w - 8]', '[356, 178, -3*w^3 + 4*w^2 + 10*w - 9]', '[356, 178, -2*w^3 + w^2 + 5*w - 2]', '[359, 359, -5/2*w^3 + 9/2*w^2 + 11/2*w - 6]', '[359, 359, -1/2*w^3 + 7/2*w^2 + 1/2*w - 6]', '[361, 19, 2*w^3 - 2*w^2 - 6*w + 1]', '[361, 19, -2*w^3 + 2*w^2 + 6*w - 3]', '[361, 361, -3/2*w^3 - 1/2*w^2 + 13/2*w + 2]', '[361, 361, 3/2*w^3 - 7/2*w^2 - 5/2*w + 8]', '[379, 379, 1/2*w^3 + 5/2*w^2 - 9/2*w - 7]', '[379, 379, w^3 - w^2 - 6*w + 3]', '[389, 389, 1/2*w^3 - 1/2*w^2 - 5/2*w - 4]', '[389, 389, w - 5]', '[400, 10, 2*w^3 - 2*w^2 - 6*w + 2]', '[400, 20, w^3 + w^2 - 4*w - 8]', '[400, 20, 1/2*w^3 + 1/2*w^2 + 1/2*w - 4]', '[401, 401, 2*w^2 + w - 7]', '[401, 401, -3/2*w^3 + 7/2*w^2 + 11/2*w - 6]', '[401, 401, w^3 - 3*w^2 - 3*w + 3]', '[401, 401, 2*w^2 - 9]', '[404, 202, -w^3 + 2*w^2 + 5*w]', '[404, 202, -5/2*w^3 + 5/2*w^2 + 21/2*w - 1]', '[404, 202, -1/2*w^3 + 3/2*w^2 + 7/2*w - 8]', '[404, 202, w^3 - w^2 - 2]', '[409, 409, -1/2*w^3 - 5/2*w^2 + 9/2*w + 8]', '[409, 409, 1/2*w^3 + 3/2*w^2 - 3/2*w - 7]', '[409, 409, -3/2*w^3 + 7/2*w^2 + 9/2*w - 5]', '[409, 409, -1/2*w^3 + 7/2*w^2 - 3/2*w - 7]', '[419, 419, 2*w^3 - 11*w - 5]', '[419, 419, 5/2*w^3 - 3/2*w^2 - 17/2*w + 2]', '[421, 421, -1/2*w^3 + 5/2*w^2 + 7/2*w - 2]', '[421, 421, -w^3 + w^2 + w + 5]', '[431, 431, 2*w^3 - w^2 - 6*w - 1]', '[431, 431, -5/2*w^3 + 7/2*w^2 + 15/2*w - 5]', '[436, 218, w^3 - 2*w^2 + w + 4]', '[436, 218, 1/2*w^3 - 5/2*w^2 + 3/2*w + 7]', '[436, 218, -w^3 - w^2 + 6*w + 2]', '[436, 218, -2*w^3 + w^2 + 8*w - 2]', '[436, 218, 2*w^3 - w^2 - 7*w + 5]', '[436, 218, -5/2*w^3 + 3/2*w^2 + 23/2*w - 2]', '[436, 218, -w^3 + 4*w^2 + 3*w - 10]', '[436, 218, -9/2*w^3 + 11/2*w^2 + 35/2*w - 12]', '[439, 439, -w^3 + 7*w - 5]', '[439, 439, -w^3 + w + 3]', '[449, 449, -2*w^3 + 2*w^2 + 5*w - 3]', '[449, 449, -1/2*w^3 - 1/2*w^2 + 11/2*w - 1]', '[449, 449, 1/2*w^3 + 1/2*w^2 - 5/2*w - 7]', '[449, 449, 5/2*w^3 - 5/2*w^2 - 11/2*w + 5]', '[464, 58, -w^3 + 3*w^2 + 3*w - 2]', '[464, 58, -2*w^2 + 10]', '[464, 116, -2*w^3 + w^2 + 6*w]', '[464, 116, -w^3 + 2*w + 4]', '[464, 116, -2*w^3 + 3*w^2 + 7*w - 3]', '[464, 116, -5/2*w^3 + 7/2*w^2 + 15/2*w - 6]', '[475, 95, 3/2*w^3 - 1/2*w^2 - 15/2*w + 2]', '[475, 95, 1/2*w^3 - 3/2*w^2 + 3/2*w + 5]', '[484, 22, 1/2*w^3 - 7/2*w^2 + 1/2*w + 10]', '[484, 22, -w^3 + 4*w^2 + 2*w - 11]', '[484, 22, -3*w^2 + 2*w + 6]', '[484, 22, 3*w^2 - w - 6]', '[491, 491, -5/2*w^3 + 5/2*w^2 + 17/2*w - 2]', '[491, 491, 2*w^3 - 2*w^2 - 5*w + 1]', '[496, 62, -2*w^3 + 4*w^2 + 6*w - 6]', '[496, 62, -w^3 - w^2 + 3*w + 6]', '[496, 124, -w^2 + 8]', '[496, 124, -3/2*w^3 + 1/2*w^2 + 17/2*w + 2]', '[496, 124, -1/2*w^3 + 3/2*w^2 + 3/2*w + 2]', '[496, 124, -w^2 + 4*w]', '[499, 499, w^3 + w^2 - 5*w - 1]', '[499, 499, -w^3 + 3*w^2 + w - 9]', '[521, 521, -w^3 + 4*w^2 + w - 9]', '[521, 521, 1/2*w^3 + 5/2*w^2 - 7/2*w - 7]', '[524, 262, 3*w^3 - 2*w^2 - 12*w - 5]', '[524, 262, w^2 + 2*w - 6]', '[524, 262, w^3 - 4*w - 7]', '[524, 262, 2*w^3 - 3*w^2 - 7*w - 2]', '[524, 262, -1/2*w^3 - 1/2*w^2 + 3/2*w + 8]', '[524, 262, w^3 - 2*w^2 - 3*w - 2]', '[524, 262, -w^3 + 2*w^2 + 2*w + 2]', '[524, 262, 5/2*w^3 - 7/2*w^2 - 11/2*w + 6]', '[541, 541, -3/2*w^3 + 5/2*w^2 + 11/2*w - 1]', '[541, 541, 1/2*w^3 + 1/2*w^2 - 1/2*w - 6]', '[551, 551, 2*w^2 - 3*w - 9]', '[551, 551, 1/2*w^3 - 7/2*w^2 - 1/2*w + 7]', '[551, 551, -1/2*w^3 + 7/2*w^2 + 1/2*w - 10]', '[551, 551, -1/2*w^3 - 3/2*w^2 + 9/2*w]', '[569, 569, -3/2*w^3 + 5/2*w^2 + 3/2*w - 5]', '[569, 569, -2*w^3 + 4*w^2 + 5*w - 13]', '[571, 571, -w^3 + 3*w^2 - 7]', '[571, 571, -w^3 + 2*w^2 + w - 7]', '[589, 589, -1/2*w^3 + 7/2*w^2 - 1/2*w - 7]', '[589, 589, -w^3 - w^2 + 2*w + 5]', '[589, 589, 5/2*w^3 - 9/2*w^2 - 17/2*w + 8]', '[589, 589, -3*w^2 + 2*w + 9]', '[596, 298, -4*w^2 + 5*w + 10]', '[596, 298, -5*w^2 + 5*w + 17]', '[596, 298, 1/2*w^3 + 1/2*w^2 - 11/2*w - 2]', '[596, 298, w^3 + 2*w^2 - 8*w - 10]', '[599, 599, 1/2*w^3 + 5/2*w^2 - 5/2*w - 11]', '[599, 599, 1/2*w^3 + 3/2*w^2 - 11/2*w - 8]', '[604, 302, -3*w^2 + w + 8]', '[604, 302, -3/2*w^3 - 1/2*w^2 + 11/2*w - 1]', '[604, 302, 1/2*w^3 - 11/2*w^2 + 5/2*w + 20]', '[604, 302, -3*w^2 + 4*w + 10]', '[619, 619, -w - 5]', '[619, 619, -1/2*w^3 + 1/2*w^2 + 5/2*w - 6]', '[619, 619, -1/2*w^3 + 7/2*w^2 - 1/2*w - 9]', '[619, 619, 3*w^2 - 2*w - 7]', '[625, 5, 5]', '[641, 641, -w^3 - 2*w^2 + 5*w + 3]', '[641, 641, 2*w^2 - 4*w - 7]', '[641, 641, 3/2*w^3 - 9/2*w^2 - 5/2*w + 13]', '[641, 641, -3/2*w^3 + 7/2*w^2 + 5/2*w - 9]', '[656, 82, -w^3 - w^2 + 5*w]', '[656, 82, -w^3 + 3*w^2 + w - 10]', '[656, 164, -5/2*w^3 + 5/2*w^2 + 21/2*w - 7]', '[656, 164, -1/2*w^3 + 7/2*w^2 - 1/2*w - 8]', '[656, 164, -w^3 + 2*w^2 + 6*w - 4]', '[656, 164, -w^3 + w^2 - 4]', '[659, 659, -w^3 + 7*w + 1]', '[659, 659, 5/2*w^3 - 5/2*w^2 - 19/2*w - 1]', '[659, 659, -1/2*w^3 + 7/2*w^2 + 1/2*w - 8]', '[659, 659, 2*w^2 + 2*w - 7]', '[661, 661, 2*w^3 - 2*w^2 - 10*w + 1]', '[661, 661, w^3 - 5*w - 7]', '[691, 691, -w^3 + 3*w^2 + 4*w - 3]', '[691, 691, -3/2*w^3 + 7/2*w^2 + 1/2*w - 6]', '[691, 691, 5/2*w^3 - 1/2*w^2 - 23/2*w - 2]', '[691, 691, -1/2*w^3 + 5/2*w^2 + 5/2*w - 10]', '[701, 701, 5/2*w^3 - 5/2*w^2 - 23/2*w + 4]', '[701, 701, -1/2*w^3 + 1/2*w^2 + 7/2*w - 7]', '[701, 701, -2*w^3 + w^2 + 10*w - 3]', '[701, 701, -1/2*w^3 + 7/2*w^2 - 3/2*w - 12]', '[709, 709, -1/2*w^3 + 5/2*w^2 - 3/2*w - 8]', '[709, 709, -3/2*w^3 + 5/2*w^2 + 5/2*w - 7]', '[719, 719, -w^3 + 4*w^2 - w - 9]', '[719, 719, 3/2*w^3 + 3/2*w^2 - 17/2*w - 5]', '[724, 362, -w^2 + w + 8]', '[724, 362, 2*w^3 - 3*w^2 - 7*w + 2]', '[724, 362, -3/2*w^3 + 7/2*w^2 + 11/2*w - 5]', '[724, 362, -w^2 + w - 3]', '[725, 145, 3/2*w^3 - 1/2*w^2 - 5/2*w - 3]', '[725, 145, 3*w^3 - 4*w^2 - 11*w + 5]', '[739, 739, 3/2*w^3 + 1/2*w^2 - 11/2*w - 8]', '[739, 739, 2*w^3 - 4*w^2 - 5*w + 3]', '[761, 761, 3*w^2 - 11]', '[761, 761, 5/2*w^3 - 7/2*w^2 - 13/2*w + 4]', '[761, 761, -3/2*w^3 + 9/2*w^2 + 9/2*w - 7]', '[761, 761, 5/2*w^3 - 3/2*w^2 - 17/2*w - 1]', '[764, 382, -2*w^3 + 2*w^2 + 9*w + 2]', '[764, 382, -4*w^3 + 3*w^2 + 17*w + 1]', '[764, 382, -1/2*w^3 - 5/2*w^2 + 11/2*w + 12]', '[764, 382, -w^2 + 4*w + 6]', '[775, 155, w^2 + 2*w - 7]', '[775, 155, 3/2*w^3 - 5/2*w^2 - 13/2*w + 1]', '[779, 779, -5/2*w^3 + 7/2*w^2 + 13/2*w - 5]', '[779, 779, -3*w^3 + 6*w^2 + 7*w - 13]', '[779, 779, 5/2*w^3 + 1/2*w^2 - 19/2*w - 3]', '[779, 779, -5/2*w^3 + 3/2*w^2 + 17/2*w]', '[821, 821, -w^3 + w^2 + 7*w + 1]', '[821, 821, -4*w - 1]', '[821, 821, -w^3 + w^2 + 7*w - 5]', '[821, 821, 2*w^3 - 2*w^2 - 10*w + 5]', '[829, 829, 3*w^3 - 2*w^2 - 11*w + 1]', '[829, 829, -5/2*w^3 + 7/2*w^2 + 11/2*w - 5]', '[839, 839, 3/2*w^3 + 1/2*w^2 - 9/2*w - 6]', '[839, 839, 5/2*w^3 - 9/2*w^2 - 15/2*w + 6]', '[841, 29, 1/2*w^3 - 1/2*w^2 - 3/2*w + 6]', '[841, 29, 5/2*w^3 - 5/2*w^2 - 15/2*w + 4]', '[841, 841, -w^3 - w^2 + 3*w + 7]', '[841, 841, -2*w^3 + 4*w^2 + 6*w - 5]', '[844, 422, -w^3 + 3*w^2 + 4*w - 2]', '[844, 422, -5/2*w^3 + 7/2*w^2 + 19/2*w - 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