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Label Polynomial Discriminant Galois group Class group
5.5.14443289801.1 x5 - x4 - 27x3 - 22x2 + 57x + 58 \( 41\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.1.28182028880.1 x5 - 274x2 + 822x + 4932 \( 2^{4}\cdot 5\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.1.31352507129.1 x5 - 2x4 + 29x3 + 98x2 - 184x + 75 \( 89\cdot 137^{4} \) $S_5$ (as 5T5) $[2]$
5.1.33818434656.1 x5 - x4 - 27x3 - 159x2 - 354x - 490 \( 2^{5}\cdot 3\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.3.85602912723.1 x5 - x4 - 164x3 + 389x2 - 80x + 332 \( -\,3^{5}\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.3.85602912723.2 x5 - 2x4 - 108x3 - 176x2 + 2830x + 5007 \( -\,3^{5}\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.1.152182955952.1 x5 - x4 - 27x3 + 115x2 - 217x + 195 \( 2^{4}\cdot 3^{3}\cdot 137^{4} \) $S_5$ (as 5T5) $[3]$
5.1.174728579056.1 x5 - 2x4 + 29x3 - 176x2 + 775x - 62 \( 2^{4}\cdot 31\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.3.237785868675.1 x5 - x4 - 27x3 - 159x2 + 57x + 3072 \( -\,3^{3}\cdot 5^{2}\cdot 137^{4} \) $S_5$ (as 5T5) $[2]$
5.3.342411650892.1 x5 - x4 - 27x3 - 159x2 - 354x - 216 \( -\,2^{2}\cdot 3^{5}\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.3.342411650892.2 x5 - x4 - 27x3 + 115x2 + 194x - 216 \( -\,2^{2}\cdot 3^{5}\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.1.704550722000.1 x5 + 1370x - 822 \( 2^{4}\cdot 5^{3}\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.1.704550722000.2 x5 - 274 \( 2^{4}\cdot 5^{3}\cdot 137^{4} \) $F_5$ (as 5T3) trivial
5.1.773948968117.1 x5 - x4 + 247x3 - 1529x2 + 5263x - 13916 \( 13^{3}\cdot 137^{4} \) $F_5$ (as 5T3) trivial
5.1.1100860503125.1 x5 - 137 \( 5^{5}\cdot 137^{4} \) $F_5$ (as 5T3) trivial
5.1.2739293207136.1 x5 - x4 - 27x3 + 389x2 - 80x + 1428 \( 2^{5}\cdot 3^{5}\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.1.3566788030125.1 x5 - 3699 \( 3^{4}\cdot 5^{3}\cdot 137^{4} \) $F_5$ (as 5T3) $[3]$
5.1.8591643779429.1 x5 - x4 - 27x3 + 5047x2 + 63625x + 209394 \( 29^{3}\cdot 137^{4} \) $F_5$ (as 5T3) trivial
5.3.17613768050000.1 x5 - 685x - 1096 \( -\,2^{4}\cdot 5^{5}\cdot 137^{4} \) $S_5$ (as 5T5) $[2]$
5.1.17613768050000.1 x5 - 2192 \( 2^{4}\cdot 5^{5}\cdot 137^{4} \) $F_5$ (as 5T3) trivial
5.1.17613768050000.2 x5 - 1096 \( 2^{4}\cdot 5^{5}\cdot 137^{4} \) $F_5$ (as 5T3) trivial
5.1.17613768050000.3 x5 - 548 \( 2^{4}\cdot 5^{5}\cdot 137^{4} \) $F_5$ (as 5T3) trivial
5.1.24279170155481.1 x5 + 137x3 - 411x2 + 137x - 49046 \( 41^{3}\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.5.24279170155481.1 x5 - x4 - 164x3 + 389x2 + 1427x + 880 \( 41^{3}\cdot 137^{4} \) $F_5$ (as 5T3) trivial
5.3.28008357127027.1 x5 - x4 - 27x3 + 937x2 - 2546x - 13916 \( -\,43^{3}\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.1.52445698919597.1 x5 - 411x3 - 1644x2 + 62883x - 435523 \( 53^{3}\cdot 137^{4} \) $F_5$ (as 5T3) trivial
5.1.57068608482000.1 x5 - 6576 \( 2^{4}\cdot 3^{4}\cdot 5^{3}\cdot 137^{4} \) $F_5$ (as 5T3) $[2]$
5.1.57068608482000.2 x5 - 4932 \( 2^{4}\cdot 3^{4}\cdot 5^{3}\cdot 137^{4} \) $F_5$ (as 5T3) $[2]$
5.1.83074984732464.1 x5 - 2x4 + 29x3 + 98x2 - 321x + 486 \( 2^{4}\cdot 3\cdot 17^{3}\cdot 137^{4} \) $S_5$ (as 5T5) trivial
5.1.89169700753125.1 x5 - 1233 \( 3^{4}\cdot 5^{5}\cdot 137^{4} \) $F_5$ (as 5T3) $[2]$
5.1.89169700753125.2 x5 - 411 \( 3^{4}\cdot 5^{5}\cdot 137^{4} \) $F_5$ (as 5T3) $[2]$
5.3.173685491712079.1 x5 - 2x4 + 166x3 + 4756x2 - 76767x - 573818 \( -\,79^{3}\cdot 137^{4} \) $S_5$ (as 5T5) trivial (GRH)
5.5.248343208968809.1 x5 - 2x4 - 382x3 + 4619x2 - 18268x + 23091 \( 89^{3}\cdot 137^{4} \) $F_5$ (as 5T3) trivial
5.1.644707945050125.1 x5 - 1507 \( 5^{3}\cdot 11^{4}\cdot 137^{4} \) $F_5$ (as 5T3) $[5]$
5.1.688037814453125.1 x5 - 3425 \( 5^{9}\cdot 137^{4} \) $F_5$ (as 5T3) $[2]$
5.1.688037814453125.2 x5 - 685 \( 5^{9}\cdot 137^{4} \) $F_5$ (as 5T3) trivial
5.1.688037814453125.3 x5 - 17125 \( 5^{9}\cdot 137^{4} \) $F_5$ (as 5T3) $[2]$ (GRH)
5.1.688037814453125.4 x5 - 17125x2 - 205500x - 4712800 \( 5^{9}\cdot 137^{4} \) $S_5$ (as 5T5) trivial (GRH)
5.1.688037814453125.5 x5 + 143850x - 295235 \( 5^{9}\cdot 137^{4} \) $S_5$ (as 5T5) $[2]$ (GRH)
5.1.688037814453125.6 x5 - 3425x2 - 37675x - 107545 \( 5^{9}\cdot 137^{4} \) $S_5$ (as 5T5) trivial (GRH)
5.1.688037814453125.7 x5 - 85625 \( 5^{9}\cdot 137^{4} \) $F_5$ (as 5T3) trivial (GRH)
5.1.688037814453125.8 x5 - 6850x2 + 44525x + 577455 \( 5^{9}\cdot 137^{4} \) $S_5$ (as 5T5) $[5]$ (GRH)
5.3.721594860791263.1 x5 - x4 - 27x3 - 707x2 + 5126x - 6655 \( -\,127^{3}\cdot 137^{4} \) $S_5$ (as 5T5) $[2]$ (GRH)
5.1.1165308928144589.1 x5 - x4 - 164x3 - 27559x2 - 210375x - 5467886 \( 137^{4}\cdot 149^{3} \) $S_5$ (as 5T5) trivial (GRH)
5.1.1165308928144589.2 x5 + 137x3 - 10686x2 + 16577x - 1017499 \( 137^{4}\cdot 149^{3} \) $F_5$ (as 5T3) trivial (GRH)
5.1.1426715212050000.1 x5 - 3288 \( 2^{4}\cdot 3^{4}\cdot 5^{5}\cdot 137^{4} \) $F_5$ (as 5T3) $[5]$
5.1.1426715212050000.2 x5 - 2466 \( 2^{4}\cdot 3^{4}\cdot 5^{5}\cdot 137^{4} \) $F_5$ (as 5T3) $[10]$
5.1.1426715212050000.3 x5 - 1644 \( 2^{4}\cdot 3^{4}\cdot 5^{5}\cdot 137^{4} \) $F_5$ (as 5T3) $[10]$
5.1.1426715212050000.4 x5 - 822 \( 2^{4}\cdot 3^{4}\cdot 5^{5}\cdot 137^{4} \) $F_5$ (as 5T3) $[5, 5]$
5.1.1691626283522000.1 x5 - 1918 \( 2^{4}\cdot 5^{3}\cdot 7^{4}\cdot 137^{4} \) $F_5$ (as 5T3) trivial
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