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Label Polynomial Discriminant Galois group Class group Regulator
5.5.13845841.1 $x^{5} - x^{4} - 24 x^{3} + 17 x^{2} + 41 x + 13$ $61^{4}$ $C_5$ (as 5T1) trivial $93.7680714453$
5.1.124612569.1 $x^{5} - x^{4} - 24 x^{3} + 17 x^{2} + 163 x - 48$ $3^{2}\cdot 61^{4}$ $D_{5}$ (as 5T2) $[5]$ $181.425128476$
5.1.664600368.1 $x^{5} - x^{4} - 24 x^{3} + 78 x^{2} - 81 x + 135$ $2^{4}\cdot 3\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $353.73018838$
5.1.775367096.1 $x^{5} - 122 x^{2} - 305 x - 854$ $2^{3}\cdot 7\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $1267.66526197$
5.3.1869188535.1 $x^{5} - 2 x^{4} - 35 x^{3} - 169 x^{2} - 76 x + 416$ $-\,3^{3}\cdot 5\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $979.115986226$
5.1.3392231045.1 $x^{5} - 122 x^{2} - 244 x - 671$ $5\cdot 7^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $380.141617842$
5.3.14178141184.1 $x^{5} - 2 x^{4} - 96 x^{3} + 136 x^{2} - 198 x - 11052$ $-\,2^{10}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $4584.19253681$
5.1.15507341920.1 $x^{5} - 2 x^{4} + 26 x^{3} - 108 x^{2} + 168 x - 560$ $2^{5}\cdot 5\cdot 7\cdot 61^{4}$ $S_5$ (as 5T5) $[10]$ $1164.458986$
5.1.16615009200.1 $x^{5} - 61 x^{3} + 1525 x - 3050$ $2^{4}\cdot 3\cdot 5^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[10]$ $892.282745578$
5.1.16961155225.1 $x^{5} - 61 x^{3} - 183 x^{2} + 61 x - 61$ $5^{2}\cdot 7^{2}\cdot 61^{4}$ $A_5$ (as 5T4) $[15]$ $139.759963136$
5.1.22153345600.2 $x^{5} - x^{4} - 24 x^{3} - 410 x^{2} + 1566 x - 2122$ $2^{6}\cdot 5^{2}\cdot 61^{4}$ $A_5$ (as 5T4) $[15]$ $1034.48783318$
5.1.23925613248.1 $x^{5} - x^{4} - 24 x^{3} - 288 x^{2} - 996 x - 3708$ $2^{6}\cdot 3^{3}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $6131.83265916$
5.3.26140947808.1 $x^{5} - 2 x^{4} + 26 x^{3} - 352 x^{2} - 3736 x + 904$ $-\,2^{5}\cdot 59\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $5123.16544386$
5.1.30419312677.2 $x^{5} - 2 x^{4} + 87 x^{3} + 624 x^{2} + 1815 x + 2063$ $13^{3}\cdot 61^{4}$ $F_5$ (as 5T3) $[10]$ $433.261740727$
5.1.43268253125.1 $x^{5} - 61$ $5^{5}\cdot 61^{4}$ $F_5$ (as 5T3) $[5]$ $1187.88895245$
5.1.43420557376.2 $x^{5} - 488 x^{2} - 1220 x - 18544$ $2^{6}\cdot 7^{2}\cdot 61^{4}$ $D_{5}$ (as 5T2) $[5]$ $3469.75137635$
5.1.44985137409.1 $x^{5} - x^{4} + 37 x^{3} + 17 x^{2} + 346 x + 257$ $3^{2}\cdot 19^{2}\cdot 61^{4}$ $A_5$ (as 5T4) $[5]$ $986.500716454$
5.1.52240358093.1 $x^{5} + 61 x^{3} - 122 x^{2} + 2928 x - 4392$ $7^{3}\cdot 11\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $2501.95219886$
5.3.53832629808.3 $x^{5} - 2 x^{4} - 96 x^{3} + 746 x^{2} - 2272 x + 2490$ $-\,2^{4}\cdot 3^{5}\cdot 61^{4}$ $S_5$ (as 5T5) $[10]$ $2274.15751979$
5.1.54954142929.1 $x^{5} - 2 x^{4} - 35 x^{3} + 197 x^{2} - 259 x + 233$ $3^{4}\cdot 7^{2}\cdot 61^{4}$ $A_5$ (as 5T4) $[5]$ $1047.07533447$
5.1.54954142929.2 $x^{5} - x^{4} - 24 x^{3} - 227 x^{2} - 1057 x - 2976$ $3^{4}\cdot 7^{2}\cdot 61^{4}$ $A_5$ (as 5T4) $[5]$ $4785.01909735$
5.1.77758243056.1 $x^{5} - 61 x^{3} - 244 x^{2} + 366 x - 854$ $2^{4}\cdot 3^{3}\cdot 13\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $6596.34889873$
5.1.79973577616.1 $x^{5} - x^{4} + 37 x^{3} + 871 x^{2} - 1484 x + 41432$ $2^{4}\cdot 19^{2}\cdot 61^{4}$ $A_5$ (as 5T4) $[10]$ $1981.33410261$
5.3.83075046000.1 $x^{5} - x^{4} - 85 x^{3} + 1115 x^{2} + 1200 x - 13590$ $-\,2^{4}\cdot 3\cdot 5^{3}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $8470.73174976$
5.1.89721049680.1 $x^{5} - x^{4} - 146 x^{3} + 200 x^{2} + 7300 x - 32500$ $2^{4}\cdot 3^{4}\cdot 5\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $9307.25796201$
5.1.100036201225.1 $x^{5} - 915 x^{2} + 2440 x - 1769$ $5^{2}\cdot 17^{2}\cdot 61^{4}$ $A_5$ (as 5T4) $[15]$ $626.822494428$
5.3.107222192704.2 $x^{5} - 2 x^{4} - 96 x^{3} - 352 x^{2} + 595 x + 4198$ $-\,2^{6}\cdot 11^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $8708.58006953$
5.1.110766728000.1 $x^{5} - 2 x^{4} + 26 x^{3} + 380 x^{2} - 2455 x + 3710$ $2^{6}\cdot 5^{3}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $3809.30727701$
5.3.112151312100.1 $x^{5} - 2 x^{4} + 87 x^{3} - 474 x^{2} - 564 x - 72$ $-\,2^{2}\cdot 3^{4}\cdot 5^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $29760.1762275$
5.1.112151312100.1 $x^{5} - 2 x^{4} - 35 x^{3} + 75 x^{2} + 900 x + 1575$ $2^{2}\cdot 3^{4}\cdot 5^{2}\cdot 61^{4}$ $A_5$ (as 5T4) $[10]$ $3192.69505794$
5.1.124958715025.1 $x^{5} - 2 x^{4} - 35 x^{3} - 657 x^{2} + 4743 x + 2673$ $5^{2}\cdot 19^{2}\cdot 61^{4}$ $D_{5}$ (as 5T2) $[5, 5]$ $1942.10113915$
5.3.127603270656.1 $x^{5} - x^{4} - 24 x^{3} - 44 x^{2} + 102 x + 562$ $-\,2^{10}\cdot 3^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $5884.40101164$
5.1.140189140125.2 $x^{5} - 305 x^{2} + 915 x - 4392$ $3^{4}\cdot 5^{3}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $3094.19321661$
5.3.149535082800.1 $x^{5} - x^{4} - 85 x^{3} - 593 x^{2} - 3436 x - 1390$ $-\,2^{4}\cdot 3^{3}\cdot 5^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $11860.510558$
5.3.149535082800.3 $x^{5} - x^{4} - 24 x^{3} + 444 x^{2} + 651 x + 135$ $-\,2^{4}\cdot 3^{3}\cdot 5^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $5153.65154329$
5.3.149535082800.4 $x^{5} - x^{4} - 24 x^{3} - 532 x^{2} + 2908 x + 318$ $-\,2^{4}\cdot 3^{3}\cdot 5^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $13313.9256267$
5.1.149535082800.1 $x^{5} - x^{4} - 24 x^{3} - 44 x^{2} + 3335 x - 8283$ $2^{4}\cdot 3^{3}\cdot 5^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $13385.2705533$
5.3.149756616256.2 $x^{5} - 2 x^{4} - 35 x^{3} - 352 x^{2} - 2516 x + 7248$ $-\,2^{6}\cdot 13^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $29765.0618716$
5.1.149756616256.1 $x^{5} - x^{4} - 85 x^{3} + 749 x^{2} - 2826 x + 5198$ $2^{6}\cdot 13^{2}\cdot 61^{4}$ $A_5$ (as 5T4) $[30]$ $1698.74476309$
5.3.161497889424.2 $x^{5} - x^{4} - 146 x^{3} + 566 x^{2} + 1993 x - 3037$ $-\,2^{4}\cdot 3^{6}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $10948.7492262$
5.5.196070954401.1 $x^{5} - 2 x^{4} - 96 x^{3} + 14 x^{2} + 1815 x + 1148$ $7^{2}\cdot 17^{2}\cdot 61^{4}$ $A_5$ (as 5T4) $[5]$ $17560.1788955$
5.3.197760147003.1 $x^{5} - x^{4} - 85 x^{3} - 105 x^{2} - 81 x - 48$ $-\,3^{3}\cdot 23^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $4459.80587566$
5.1.209473728489.1 $x^{5} - x^{4} + 37 x^{3} - 44 x^{2} + 224 x - 12248$ $3^{2}\cdot 41^{2}\cdot 61^{4}$ $D_{5}$ (as 5T2) $[5]$ $9763.008159181416$
5.3.219816571716.1 $x^{5} - 549 x^{2} - 4392 x + 2928$ $-\,2^{2}\cdot 3^{4}\cdot 7^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[10]$ $5188.8118831$
5.5.249225138000.1 $x^{5} - x^{4} - 146 x^{3} + 1054 x^{2} - 2521 x + 1843$ $2^{4}\cdot 3^{2}\cdot 5^{3}\cdot 61^{4}$ $F_5$ (as 5T3) $[5]$ $8191.92830387$
5.1.269163149040.1 $x^{5} - 2 x^{4} + 87 x^{3} + 258 x^{2} - 1479 x - 6660$ $2^{4}\cdot 3^{5}\cdot 5\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $11661.697979$
5.1.292493391125.2 $x^{5} - 1220 x^{2} - 3660 x - 43371$ $5^{3}\cdot 13^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $3000.30186152$
5.1.292493391125.3 $x^{5} - 2 x^{4} - 35 x^{3} + 990 x^{2} + 1205 x - 34415$ $5^{3}\cdot 13^{2}\cdot 61^{4}$ $F_5$ (as 5T3) $[5]$ $3425.30825714$
5.3.293088762288.3 $x^{5} - 2 x^{4} - 96 x^{3} + 1234 x^{2} + 6451 x + 7248$ $-\,2^{4}\cdot 3^{3}\cdot 7^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $13785.0449896$
5.1.293088762288.1 $x^{5} - 61 x^{3} - 1342 x^{2} - 3843 x - 35258$ $2^{4}\cdot 3^{3}\cdot 7^{2}\cdot 61^{4}$ $S_5$ (as 5T5) $[5]$ $5083.50823531$
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