Database - hmf_fields (Information on base fields for Hilbert modular forms)

Formats: - HTML - YAML - JSON - 2026-04-29T18:48:52.560460

Query: /api/hmf_fields/?_offset=0

Column	Type
degree	smallint
discriminant	bigint
ideals	jsonb
label	text
narrow_class_no	smallint
primes	jsonb

{'degree': 4, 'discriminant': 4525, 'id': 78, 'ideals': ['[1, 1, 1]', '[5, 5, -1/3*w^3 - 2/3*w^2 + 7/3*w + 4]', '[5, 5, 1/3*w^3 - 4/3*w^2 - 1/3*w + 3]', '[9, 3, -w]', '[9, 3, 1/3*w^3 - 1/3*w^2 - 7/3*w + 1]', '[16, 2, 2]', '[19, 19, 2/3*w^3 - 2/3*w^2 - 11/3*w]', '[19, 19, -1/3*w^3 + 1/3*w^2 + 1/3*w + 1]', '[25, 5, 1/3*w^3 + 2/3*w^2 - 7/3*w - 2]', '[25, 5, -2/3*w^3 + 2/3*w^2 + 8/3*w - 1]', '[25, 5, 2/3*w^3 - 2/3*w^2 - 11/3*w + 3]', '[31, 31, 2/3*w^3 + 1/3*w^2 - 11/3*w - 2]', '[31, 31, 2/3*w^3 - 5/3*w^2 - 5/3*w + 5]', '[41, 41, -1/3*w^3 + 4/3*w^2 + 7/3*w - 6]', '[41, 41, -1/3*w^3 + 4/3*w^2 + 7/3*w - 3]', '[45, 15, -w - 3]', '[45, 15, -1/3*w^3 + 4/3*w^2 + 4/3*w - 2]', '[45, 15, -w^2 + 6]', '[45, 15, -1/3*w^3 + 1/3*w^2 + 7/3*w - 4]', '[61, 61, 1/3*w^3 - 4/3*w^2 + 2/3*w + 4]', '[61, 61, 2/3*w^3 + 1/3*w^2 - 14/3*w - 2]', '[71, 71, -1/3*w^3 + 4/3*w^2 + 1/3*w - 7]', '[71, 71, 1/3*w^3 + 2/3*w^2 - 7/3*w]', '[80, 10, -2/3*w^3 - 4/3*w^2 + 14/3*w + 8]', '[80, 10, 2/3*w^3 - 8/3*w^2 - 2/3*w + 6]', '[81, 3, 3]', '[81, 9, w^2]', '[81, 9, 1/3*w^3 - 4/3*w^2 - 4/3*w + 8]', '[89, 89, -1/3*w^3 + 1/3*w^2 + 10/3*w - 3]', '[89, 89, 1/3*w^3 - 1/3*w^2 - 10/3*w - 1]', '[95, 95, -2/3*w^3 - 1/3*w^2 + 11/3*w + 1]', '[95, 95, -2/3*w^3 + 5/3*w^2 + 5/3*w - 6]', '[95, 95, 2*w + 1]', '[95, 95, 2/3*w^3 - 2/3*w^2 - 14/3*w + 3]', '[101, 101, 1/3*w^3 - 1/3*w^2 - 7/3*w - 3]', '[101, 101, -2/3*w^3 + 5/3*w^2 + 11/3*w - 4]', '[101, 101, 2/3*w^3 - 5/3*w^2 - 8/3*w + 3]', '[101, 101, w - 4]', '[109, 109, 2/3*w^3 + 1/3*w^2 - 8/3*w - 4]', '[109, 109, -w^3 + 2*w^2 + 4*w - 4]', '[121, 11, w^3 - w^2 - 4*w + 1]', '[121, 11, -w^3 + w^2 + 4*w - 2]', '[125, 5, 1/3*w^3 - 4/3*w^2 + 5/3*w + 1]', '[125, 5, -w^3 + 7*w + 4]', '[125, 25, -1/3*w^3 + 4/3*w^2 + 1/3*w]', '[125, 25, -1/3*w^3 - 2/3*w^2 + 7/3*w + 7]', '[131, 131, 4/3*w^3 - 1/3*w^2 - 22/3*w - 1]', '[131, 131, -w^3 + 7*w + 2]', '[139, 139, 2/3*w^3 - 2/3*w^2 - 14/3*w + 1]', '[139, 139, 2*w - 1]', '[139, 139, 1/3*w^3 + 5/3*w^2 - 7/3*w - 10]', '[139, 139, -2/3*w^3 + 8/3*w^2 + 5/3*w - 5]', '[144, 6, -2*w]', '[144, 6, 2/3*w^3 - 2/3*w^2 - 14/3*w + 2]', '[149, 149, w^3 + w^2 - 7*w - 11]', '[149, 149, -w^3 - w^2 + 5*w + 4]', '[151, 151, -2/3*w^3 - 4/3*w^2 + 14/3*w + 5]', '[151, 151, 2/3*w^3 - 8/3*w^2 - 2/3*w + 9]', '[155, 155, -1/3*w^3 - 2/3*w^2 + 4/3*w + 6]', '[155, 155, -1/3*w^3 + 1/3*w^2 + 10/3*w - 2]', '[155, 155, 1/3*w^3 - 1/3*w^2 - 10/3*w]', '[155, 155, 2/3*w^3 - 5/3*w^2 - 8/3*w + 2]', '[169, 13, -2/3*w^3 - 1/3*w^2 + 11/3*w]', '[169, 13, -2/3*w^3 + 5/3*w^2 + 5/3*w - 7]', '[171, 57, -1/3*w^3 + 7/3*w^2 + 1/3*w - 6]', '[171, 57, 1/3*w^3 + 2/3*w^2 - 10/3*w]', '[171, 57, -w^2 + 2*w + 6]', '[171, 57, -2*w^2 + w + 9]', '[179, 179, 4/3*w^3 - 7/3*w^2 - 13/3*w + 6]', '[179, 179, -4/3*w^3 + 1/3*w^2 + 19/3*w + 1]', '[181, 181, 5/3*w^3 - 8/3*w^2 - 20/3*w + 5]', '[181, 181, -1/3*w^3 + 1/3*w^2 + 10/3*w - 1]', '[181, 181, -4/3*w^3 + 1/3*w^2 + 16/3*w + 3]', '[191, 191, w^2 - 3*w - 1]', '[191, 191, -1/3*w^3 + 4/3*w^2 + 10/3*w - 3]', '[199, 199, -w^3 + 3*w^2 + w - 7]', '[199, 199, -4/3*w^3 + 1/3*w^2 + 19/3*w - 1]', '[205, 205, -5/3*w^3 + 11/3*w^2 + 14/3*w - 10]', '[205, 205, -5/3*w^3 - 1/3*w^2 + 26/3*w + 4]', '[205, 205, -2/3*w^3 + 5/3*w^2 + 5/3*w - 8]', '[205, 205, -2/3*w^3 - 1/3*w^2 + 11/3*w - 1]', '[211, 211, -1/3*w^3 - 5/3*w^2 + 4/3*w + 8]', '[211, 211, w^3 - 3*w^2 - 4*w + 8]', '[225, 15, -1/3*w^3 + 7/3*w^2 + 1/3*w - 9]', '[225, 15, -w^3 + w^2 + 6*w - 6]', '[225, 15, -w^3 + 2*w^2 + 4*w - 3]', '[225, 15, -2/3*w^3 - 1/3*w^2 + 8/3*w + 5]', '[225, 15, 2*w^2 - w - 6]', '[225, 15, -w^3 - w^2 + 6*w + 5]', '[229, 229, -4/3*w^3 + 4/3*w^2 + 13/3*w - 4]', '[229, 229, -5/3*w^3 + 5/3*w^2 + 23/3*w - 5]', '[229, 229, 1/3*w^3 - 7/3*w^2 + 2/3*w + 10]', '[229, 229, -2/3*w^3 + 2/3*w^2 + 2/3*w - 3]', '[239, 239, 4/3*w^3 - 1/3*w^2 - 19/3*w - 2]', '[239, 239, -2/3*w^3 + 2/3*w^2 + 11/3*w - 6]', '[251, 251, 2*w^2 - w - 8]', '[251, 251, -1/3*w^3 - 2/3*w^2 + 7/3*w - 2]', '[251, 251, 1/3*w^3 - 4/3*w^2 - 1/3*w + 9]', '[251, 251, -1/3*w^3 + 7/3*w^2 + 1/3*w - 7]', '[256, 4, 4]', '[269, 269, -5/3*w^3 + 8/3*w^2 + 17/3*w - 8]', '[269, 269, -5/3*w^3 + 11/3*w^2 + 17/3*w - 12]', '[271, 271, 1/3*w^3 + 2/3*w^2 - 13/3*w - 3]', '[271, 271, 1/3*w^3 + 2/3*w^2 - 13/3*w - 2]', '[279, 93, w^3 - 3*w^2 - 3*w + 12]', '[279, 93, -2/3*w^3 - 4/3*w^2 + 11/3*w + 9]', '[279, 93, 2/3*w^3 + 4/3*w^2 - 11/3*w - 3]', '[279, 93, w^3 - 3*w^2 - 3*w + 6]', '[304, 38, 4/3*w^3 - 4/3*w^2 - 22/3*w]', '[304, 38, -2/3*w^3 + 2/3*w^2 + 2/3*w + 2]', '[305, 305, -5/3*w^3 - 1/3*w^2 + 26/3*w + 9]', '[305, 305, -2*w^3 + 5*w^2 + 2*w - 5]', '[305, 305, 3*w^3 - 18*w - 13]', '[305, 305, 5/3*w^3 - 11/3*w^2 - 14/3*w + 5]', '[311, 311, -1/3*w^3 + 7/3*w^2 - 5/3*w - 8]', '[311, 311, -w^3 + 5*w - 1]', '[331, 331, -2/3*w^3 - 1/3*w^2 + 8/3*w + 6]', '[331, 331, -w^3 + 2*w^2 + 4*w - 2]', '[349, 349, -w^3 + 2*w^2 + w + 1]', '[349, 349, 1/3*w^3 - 1/3*w^2 - 7/3*w - 4]', '[349, 349, -4/3*w^3 + 13/3*w^2 + 10/3*w - 11]', '[349, 349, w - 5]', '[355, 355, 2/3*w^3 - 5/3*w^2 - 11/3*w + 2]', '[355, 355, 5/3*w^3 - 17/3*w^2 - 8/3*w + 10]', '[355, 355, 5/3*w^3 + 7/3*w^2 - 32/3*w - 18]', '[355, 355, w^2 + w - 7]', '[361, 19, 4/3*w^3 - 4/3*w^2 - 16/3*w + 1]', '[361, 19, -4/3*w^3 + 4/3*w^2 + 16/3*w - 3]', '[361, 361, 2/3*w^3 + 1/3*w^2 - 5/3*w - 4]', '[361, 361, 4/3*w^3 - 7/3*w^2 - 19/3*w + 5]', '[369, 123, -2*w^3 + 3*w^2 + 10*w - 13]', '[369, 123, -w^3 + 2*w - 3]', '[369, 123, -w^3 + 5*w - 3]', '[369, 123, -w^3 + 2*w^2 + 3*w - 10]', '[379, 379, 7/3*w^3 - 1/3*w^2 - 43/3*w - 9]', '[379, 379, 2*w^3 - 3*w^2 - 9*w + 8]', '[400, 10, 2/3*w^3 + 4/3*w^2 - 14/3*w - 4]', '[400, 10, -4/3*w^3 + 4/3*w^2 + 16/3*w - 2]', '[400, 10, 4/3*w^3 - 4/3*w^2 - 22/3*w + 6]', '[401, 401, 1/3*w^3 + 2/3*w^2 - 7/3*w - 8]', '[401, 401, -1/3*w^3 + 10/3*w^2 - 2/3*w - 15]', '[401, 401, -4/3*w^3 + 4/3*w^2 + 13/3*w - 3]', '[401, 401, -1/3*w^3 + 4/3*w^2 - 5/3*w + 3]', '[405, 15, -w^3 - 2*w^2 + 7*w + 12]', '[405, 15, w^3 - 4*w^2 - w + 9]', '[405, 45, -w^2 + 9]', '[405, 45, w^3 - 6*w]', '[405, 45, -2/3*w^3 + 5/3*w^2 + 2/3*w - 6]', '[405, 45, -1/3*w^3 + 4/3*w^2 + 4/3*w + 1]', '[409, 409, -5/3*w^3 + 8/3*w^2 + 20/3*w - 7]', '[409, 409, 4/3*w^3 - 1/3*w^2 - 16/3*w - 1]', '[419, 419, 4/3*w^3 - 16/3*w^2 - 1/3*w + 10]', '[419, 419, 5/3*w^3 + 7/3*w^2 - 35/3*w - 17]', '[421, 421, -2*w^3 + 4*w^2 + 7*w - 10]', '[421, 421, -5/3*w^3 + 8/3*w^2 + 29/3*w - 7]', '[421, 421, 1/3*w^3 + 2/3*w^2 + 5/3*w - 4]', '[421, 421, -5/3*w^3 - 1/3*w^2 + 23/3*w + 5]', '[431, 431, -2/3*w^3 + 5/3*w^2 + 11/3*w - 1]', '[431, 431, -w^2 - w + 8]', '[439, 439, -2/3*w^3 + 11/3*w^2 - 1/3*w - 8]', '[439, 439, -2/3*w^3 + 11/3*w^2 + 8/3*w - 15]', '[445, 445, -5/3*w^3 + 5/3*w^2 + 23/3*w - 2]', '[445, 445, 4/3*w^3 - 4/3*w^2 - 13/3*w + 1]', '[445, 445, 3*w^3 + w^2 - 17*w - 14]', '[445, 445, -8/3*w^3 + 20/3*w^2 + 17/3*w - 13]', '[475, 95, -2/3*w^3 + 2/3*w^2 + 17/3*w + 1]', '[475, 95, 2*w^2 - 3*w - 2]', '[475, 95, 2/3*w^3 + 4/3*w^2 - 11/3*w - 10]', '[475, 95, 1/3*w^3 - 1/3*w^2 - 13/3*w + 4]', '[475, 95, -1/3*w^3 - 5/3*w^2 + 13/3*w + 11]', '[475, 95, -w^3 + 3*w^2 + 3*w - 5]', '[479, 479, w^3 + 2*w^2 - 6*w - 10]', '[479, 479, -5/3*w^3 + 5/3*w^2 + 14/3*w]', '[479, 479, -5/3*w^3 + 5/3*w^2 + 23/3*w - 3]', '[479, 479, -4/3*w^3 + 4/3*w^2 + 13/3*w - 2]', '[496, 62, 4/3*w^3 + 2/3*w^2 - 22/3*w - 4]', '[496, 62, 4/3*w^3 - 10/3*w^2 - 10/3*w + 10]', '[505, 505, 4/3*w^3 + 2/3*w^2 - 25/3*w - 5]', '[505, 505, 1/3*w^3 + 8/3*w^2 - 13/3*w - 13]', '[505, 505, 8/3*w^3 + 7/3*w^2 - 50/3*w - 19]', '[505, 505, -2*w^3 + 11*w + 4]', '[505, 505, -2/3*w^3 + 11/3*w^2 - 7/3*w - 4]', '[505, 505, -7/3*w^3 + 22/3*w^2 + 10/3*w - 15]', '[505, 505, -1/3*w^3 + 10/3*w^2 - 5/3*w - 8]', '[505, 505, -2/3*w^3 - 1/3*w^2 + 14/3*w - 2]', '[521, 521, -w^3 + 2*w^2 + 5*w + 1]', '[521, 521, 1/3*w^3 + 2/3*w^2 - 1/3*w - 10]', '[541, 541, 1/3*w^3 + 5/3*w^2 + 2/3*w - 7]', '[541, 541, 5/3*w^3 - 5/3*w^2 - 26/3*w]', '[545, 545, 2/3*w^3 - 11/3*w^2 + 10/3*w + 3]', '[545, 545, -w^3 + 3*w^2 - 7]', '[545, 545, -5/3*w^3 - 1/3*w^2 + 32/3*w + 5]', '[545, 545, 5/3*w^3 + 4/3*w^2 - 38/3*w - 15]', '[549, 183, 4/3*w^3 - 7/3*w^2 - 16/3*w + 2]', '[549, 183, -w^3 + 4*w + 6]', '[549, 183, w^3 - 3*w^2 - 3*w + 3]', '[549, 183, -2/3*w^3 - 4/3*w^2 + 11/3*w + 12]', '[569, 569, -w - 5]', '[569, 569, 1/3*w^3 - 1/3*w^2 - 7/3*w + 6]', '[571, 571, w^3 - 4*w - 8]', '[571, 571, -1/3*w^3 + 7/3*w^2 + 7/3*w - 4]', '[589, 589, 2/3*w^3 - 5/3*w^2 - 14/3*w + 1]', '[589, 589, -1/3*w^3 + 4/3*w^2 + 10/3*w - 9]', '[589, 589, -3*w - 1]', '[589, 589, w^3 - w^2 - 7*w + 4]', '[599, 599, 5/3*w^3 - 5/3*w^2 - 14/3*w + 4]', '[599, 599, -4/3*w^3 + 13/3*w^2 + 13/3*w - 15]', '[599, 599, 2*w^3 - 3*w^2 - 8*w + 5]', '[599, 599, 7/3*w^3 - 7/3*w^2 - 34/3*w + 6]', '[601, 601, -4/3*w^3 + 13/3*w^2 + 13/3*w - 13]', '[601, 601, -w^3 + 8*w + 5]', '[605, 55, 5/3*w^3 + 1/3*w^2 - 35/3*w - 8]', '[605, 55, -4/3*w^3 + 1/3*w^2 + 28/3*w + 4]', '[605, 55, -2/3*w^3 + 8/3*w^2 - 7/3*w - 3]', '[605, 55, 1/3*w^3 - 4/3*w^2 + 8/3*w]', '[619, 619, -5/3*w^3 + 11/3*w^2 + 17/3*w - 13]', '[619, 619, 4/3*w^3 + 2/3*w^2 - 19/3*w - 2]', '[625, 5, 5]', '[625, 25, -2/3*w^3 + 2/3*w^2 + 17/3*w - 4]', '[625, 25, -1/3*w^3 + 1/3*w^2 + 13/3*w + 1]', '[625, 25, -4/3*w^3 + 10/3*w^2 + 13/3*w - 13]', '[625, 25, -1/3*w^3 + 4/3*w^2 - 5/3*w - 6]', '[631, 631, w^3 - w^2 - 7*w + 1]', '[631, 631, 3*w - 2]', '[639, 213, -w^3 + w + 3]', '[639, 213, -7/3*w^3 + 10/3*w^2 + 37/3*w - 8]', '[639, 213, -w^3 + 2*w^2 + 6*w - 3]', '[639, 213, -w^2 - 2*w + 7]', '[641, 641, -2/3*w^3 + 5/3*w^2 + 2/3*w - 7]', '[641, 641, -1/3*w^3 + 7/3*w^2 - 5/3*w - 9]', '[655, 655, 4*w^3 - 25*w - 17]', '[655, 655, -14/3*w^3 - 1/3*w^2 + 83/3*w + 20]', '[655, 655, 4/3*w^3 - 7/3*w^2 - 19/3*w + 4]', '[655, 655, -7/3*w^3 + 13/3*w^2 + 22/3*w - 6]', '[656, 82, -2/3*w^3 + 8/3*w^2 + 14/3*w - 12]', '[656, 82, -2/3*w^3 + 8/3*w^2 + 14/3*w - 6]', '[661, 661, -5/3*w^3 + 11/3*w^2 + 20/3*w - 9]', '[661, 661, w^3 + w^2 - 4*w - 7]', '[691, 691, -5/3*w^3 + 8/3*w^2 + 17/3*w - 6]', '[691, 691, 2*w^2 - 3*w - 10]', '[691, 691, 5/3*w^3 - 2/3*w^2 - 23/3*w - 1]', '[691, 691, 1/3*w^3 + 5/3*w^2 - 13/3*w - 3]', '[695, 695, -7/3*w^3 + 16/3*w^2 + 13/3*w - 9]', '[695, 695, -5/3*w^3 + 2/3*w^2 + 23/3*w + 2]', '[695, 695, 2*w^3 - 8*w^2 + w + 10]', '[695, 695, 5/3*w^3 - 8/3*w^2 - 17/3*w + 5]', '[695, 695, -2/3*w^3 - 4/3*w^2 + 14/3*w + 3]', '[695, 695, 3*w^3 - 17*w - 10]', '[695, 695, -2/3*w^3 + 8/3*w^2 + 2/3*w - 11]', '[695, 695, 3*w^3 + 3*w^2 - 21*w - 29]', '[701, 701, 2/3*w^3 + 4/3*w^2 - 20/3*w - 11]', '[701, 701, -2/3*w^3 - 1/3*w^2 + 17/3*w + 9]', '[709, 709, -2/3*w^3 - 7/3*w^2 + 17/3*w + 11]', '[709, 709, -1/3*w^3 + 10/3*w^2 - 2/3*w - 8]', '[709, 709, -2/3*w^3 + 11/3*w^2 - 1/3*w - 10]', '[709, 709, 3*w^2 - 2*w - 14]', '[719, 719, 7/3*w^3 + 8/3*w^2 - 46/3*w - 21]', '[719, 719, -2*w^3 + 7*w^2 + 2*w - 13]', '[719, 719, 2/3*w^3 + 7/3*w^2 - 14/3*w - 9]', '[719, 719, -w^3 + 4*w^2 + 2*w - 13]', '[720, 30, -2*w - 6]', '[720, 30, -2/3*w^3 + 8/3*w^2 + 8/3*w - 4]', '[720, 30, -2*w^2 + 12]', '[720, 30, -2/3*w^3 + 2/3*w^2 + 14/3*w - 8]', '[729, 9, -3*w]', '[729, 9, w^3 - w^2 - 7*w + 3]', '[729, 27, 2*w^3 - 10*w - 5]', '[729, 27, 2*w^3 - 4*w^2 - 6*w + 9]', '[745, 745, w^3 - w^2 - 7*w + 2]', '[745, 745, -2/3*w^3 + 8/3*w^2 + 8/3*w - 3]', '[745, 745, -7/3*w^3 + 13/3*w^2 + 34/3*w - 13]', '[745, 745, -7/3*w^3 + 1/3*w^2 + 49/3*w + 13]', '[755, 755, -3*w^3 + 19*w + 16]', '[755, 755, -5/3*w^3 + 14/3*w^2 + 11/3*w - 5]', '[755, 755, -5/3*w^3 - 4/3*w^2 + 29/3*w + 16]', '[755, 755, -5/3*w^3 + 14/3*w^2 - 1/3*w - 1]', '[761, 761, 1/3*w^3 + 5/3*w^2 - 1/3*w - 8]', '[761, 761, 5/3*w^3 - 2/3*w^2 - 14/3*w + 1]', '[761, 761, -8/3*w^3 + 11/3*w^2 + 38/3*w - 11]', '[761, 761, -4/3*w^3 + 10/3*w^2 + 19/3*w - 9]', '[775, 155, -2*w^3 + w^2 + 10*w + 2]', '[775, 155, 1/3*w^3 - 10/3*w^2 + 2/3*w + 14]', '[775, 155, w^2 - 3*w - 8]', '[775, 155, 5/3*w^3 - 8/3*w^2 - 14/3*w + 4]', '[775, 155, 3*w^2 - 2*w - 8]', '[775, 155, -2/3*w^3 - 1/3*w^2 + 17/3*w - 3]', '[779, 779, -7/3*w^3 + 10/3*w^2 + 31/3*w - 11]', '[779, 779, -2/3*w^3 - 1/3*w^2 + 14/3*w - 5]', '[779, 779, -1/3*w^3 + 4/3*w^2 - 2/3*w - 11]', '[779, 779, -5/3*w^3 + 2/3*w^2 + 17/3*w - 2]', '[801, 267, -w^2 + 2*w - 3]', '[801, 267, -w^3 + 2*w^2 + 6*w - 13]', '[801, 267, -1/3*w^3 - 2/3*w^2 + 10/3*w + 9]', '[801, 267, w^2 + 2*w + 3]', '[809, 809, -2/3*w^3 + 11/3*w^2 + 5/3*w - 15]', '[809, 809, 3*w^2 - w - 8]', '[811, 811, 2/3*w^3 + 7/3*w^2 - 14/3*w - 11]', '[811, 811, 1/3*w^3 + 8/3*w^2 - 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