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Note: Search results may be incomplete due to uncomputed quantities: Class number (201181 objects)

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Ramified prime count Ramified Unramified primes Galois group Is Galois
Discriminant Root discriminant Regulator Intermediate field $p$-adic completions
Monogenic Index Ines. \(p\)
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Results (1-50 of at least 1000)

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Label Polynomial Discriminant Galois group Class group Regulator
2.0.231.1 x2 - x + 58 $-\,3\cdot 7\cdot 11$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.255.1 x2 - x + 64 $-\,3\cdot 5\cdot 17$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.327.1 x2 - x + 82 $-\,3\cdot 109$ $C_2$ (as 2T1) $[12]$ $1$
2.0.356.1 x2 + 89 $-\,2^{2}\cdot 89$ $C_2$ (as 2T1) $[12]$ $1$
2.0.440.1 x2 + 110 $-\,2^{3}\cdot 5\cdot 11$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.516.1 x2 + 129 $-\,2^{2}\cdot 3\cdot 43$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.543.1 x2 - x + 136 $-\,3\cdot 181$ $C_2$ (as 2T1) $[12]$ $1$
2.0.655.1 x2 - x + 164 $-\,5\cdot 131$ $C_2$ (as 2T1) $[12]$ $1$
2.0.680.1 x2 + 170 $-\,2^{3}\cdot 5\cdot 17$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.687.1 x2 - x + 172 $-\,3\cdot 229$ $C_2$ (as 2T1) $[12]$ $1$
2.0.696.1 x2 + 174 $-\,2^{3}\cdot 3\cdot 29$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.728.1 x2 + 182 $-\,2^{3}\cdot 7\cdot 13$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.731.1 x2 - x + 183 $-\,17\cdot 43$ $C_2$ (as 2T1) $[12]$ $1$
2.0.744.1 x2 + 186 $-\,2^{3}\cdot 3\cdot 31$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.755.1 x2 - x + 189 $-\,5\cdot 151$ $C_2$ (as 2T1) $[12]$ $1$
2.0.804.1 x2 + 201 $-\,2^{2}\cdot 3\cdot 67$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.888.1 x2 + 222 $-\,2^{3}\cdot 3\cdot 37$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.932.1 x2 + 233 $-\,2^{2}\cdot 233$ $C_2$ (as 2T1) $[12]$ $1$
2.0.948.1 x2 + 237 $-\,2^{2}\cdot 3\cdot 79$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.964.1 x2 + 241 $-\,2^{2}\cdot 241$ $C_2$ (as 2T1) $[12]$ $1$
2.0.984.1 x2 + 246 $-\,2^{3}\cdot 3\cdot 41$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.996.1 x2 + 249 $-\,2^{2}\cdot 3\cdot 83$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1011.1 x2 - x + 253 $-\,3\cdot 337$ $C_2$ (as 2T1) $[12]$ $1$
2.0.1067.1 x2 - x + 267 $-\,11\cdot 97$ $C_2$ (as 2T1) $[12]$ $1$
2.0.1096.1 x2 + 274 $-\,2^{3}\cdot 137$ $C_2$ (as 2T1) $[12]$ $1$
2.0.1144.1 x2 + 286 $-\,2^{3}\cdot 11\cdot 13$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1208.1 x2 + 302 $-\,2^{3}\cdot 151$ $C_2$ (as 2T1) $[12]$ $1$
2.0.1235.1 x2 - x + 309 $-\,5\cdot 13\cdot 19$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1236.1 x2 + 309 $-\,2^{2}\cdot 3\cdot 103$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1255.1 x2 - x + 314 $-\,5\cdot 251$ $C_2$ (as 2T1) $[12]$ $1$
2.0.1272.1 x2 + 318 $-\,2^{3}\cdot 3\cdot 53$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1336.1 x2 + 334 $-\,2^{3}\cdot 167$ $C_2$ (as 2T1) $[12]$ $1$
2.0.1355.1 x2 - x + 339 $-\,5\cdot 271$ $C_2$ (as 2T1) $[12]$ $1$
2.0.1371.1 x2 - x + 343 $-\,3\cdot 457$ $C_2$ (as 2T1) $[12]$ $1$
2.0.1419.1 x2 - x + 355 $-\,3\cdot 11\cdot 43$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1464.1 x2 + 366 $-\,2^{3}\cdot 3\cdot 61$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1480.1 x2 + 370 $-\,2^{3}\cdot 5\cdot 37$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1491.1 x2 - x + 373 $-\,3\cdot 7\cdot 71$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1515.1 x2 - x + 379 $-\,3\cdot 5\cdot 101$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1547.1 x2 - x + 387 $-\,7\cdot 13\cdot 17$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1572.1 x2 + 393 $-\,2^{2}\cdot 3\cdot 131$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1668.1 x2 + 417 $-\,2^{2}\cdot 3\cdot 139$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1720.1 x2 + 430 $-\,2^{3}\cdot 5\cdot 43$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1732.1 x2 + 433 $-\,2^{2}\cdot 433$ $C_2$ (as 2T1) $[12]$ $1$
2.0.1763.1 x2 - x + 441 $-\,41\cdot 43$ $C_2$ (as 2T1) $[12]$ $1$
2.0.1807.1 x2 - x + 452 $-\,13\cdot 139$ $C_2$ (as 2T1) $[12]$ $1$
2.0.1812.1 x2 + 453 $-\,2^{2}\cdot 3\cdot 151$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1892.1 x2 + 473 $-\,2^{2}\cdot 11\cdot 43$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1955.1 x2 - x + 489 $-\,5\cdot 17\cdot 23$ $C_2$ (as 2T1) $[2, 6]$ $1$
2.0.1972.1 x2 + 493 $-\,2^{2}\cdot 17\cdot 29$ $C_2$ (as 2T1) $[2, 6]$ $1$
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