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Results (33 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
13.1.201...536.1	$x^{13} - 3 x^{12} - 4 x^{11} + 36 x^{10} + 126 x^{9} - 98 x^{8} - 932 x^{7} + 2596 x^{6} - 1175 x^{5} - 6579 x^{4} + 42960 x^{3} - 17440 x^{2} - 55232 x + 90176$	$13$	[1,6]	$2^{12}\cdot 53^{12}$	$2$	$74.04796137497303$	$78.10327769094482$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$143626578.18118104$
13.1.430...489.1	$x^{13} - 3 x^{12} - 8 x^{11} + 104 x^{10} - 692 x^{9} + 3428 x^{8} - 8262 x^{7} + 6914 x^{6} + 4464 x^{5} - 53952 x^{4} + 102420 x^{3} + 67140 x^{2} - 146259 x + 48033$	$13$	[1,6]	$3^{6}\cdot 79^{12}$	$2$	$93.7271877654942$	$97.77242883415123$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$398864627.1831563$
13.1.577...009.1	$x^{13} - 2 x^{12} + 10 x^{11} - 60 x^{10} + 19 x^{9} - 55 x^{8} + 1286 x^{7} - 5877 x^{6} + 11378 x^{5} - 22577 x^{4} + 58759 x^{3} - 216048 x^{2} - 152278 x - 2208381$	$13$	[1,6]	$7^{6}\cdot 53^{12}$	$2$	$95.870394283159$	$103.32092467462952$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$25402745.97030467$
13.1.870...601.1	$x^{13} - 2 x^{12} + 10 x^{11} - 7 x^{10} + 284 x^{9} - 532 x^{8} + 491 x^{7} + 17178 x^{6} - 75330 x^{5} + 318955 x^{4} - 942676 x^{3} + 2527868 x^{2} - 4563680 x + 4699904$	$13$	[1,6]	$11^{6}\cdot 53^{12}$	$2$	$118.10874152018647$	$129.5196334988997$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$198841510.74740678$
13.1.559...625.1	$x^{13} - 6 x^{12} - 16 x^{11} + 129 x^{10} - 51 x^{9} - 804 x^{8} + 3422 x^{7} - 393 x^{6} - 22868 x^{5} + 33357 x^{4} + 64269 x^{3} - 108540 x^{2} - 133650 x + 273375$	$13$	[1,6]	$3^{6}\cdot 5^{6}\cdot 53^{12}$	$3$	$136.2858021180073$	$151.24634689062128$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$1898111991.9739501$
13.1.695...209.1	$x^{13} - x^{12} + 43 x^{11} + 156 x^{10} + 760 x^{9} + 2994 x^{8} + 6335 x^{7} + 6568 x^{6} - 31037 x^{5} - 134767 x^{4} - 205952 x^{3} - 182000 x^{2} + 730450 x + 2750125$	$13$	[1,6]	$7^{6}\cdot 79^{12}$	$2$	$138.58014959554995$	$149.34985200406032$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$297908147.0846002$
13.1.938...616.1	$x^{13} - x^{12} + 29 x^{11} - 193 x^{10} + 455 x^{9} + 3965 x^{8} - 34733 x^{7} + 217281 x^{6} - 913512 x^{5} + 3364596 x^{4} - 8558784 x^{3} + 14279328 x^{2} - 11819520 x + 4478976$	$13$	[1,6]	$2^{18}\cdot 3^{6}\cdot 53^{12}$	$3$	$169.30112240939073$	$191.31317758171556$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$154940012974.86566$
13.1.163...129.1	$x^{13} - 3 x^{12} - 20 x^{11} + 29 x^{10} - 530 x^{9} + 8831 x^{8} - 58416 x^{7} + 223607 x^{6} - 275895 x^{5} - 124008 x^{4} + 433260 x^{3} + 2144088 x^{2} - 22064832 x + 119799648$	$13$	[1,6]	$3^{6}\cdot 157^{12}$	$2$	$176.6827313406098$	$184.30831211371242$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$29324963808.316612$
13.1.395...169.1	$x^{13} - 65 x^{11} - 403 x^{10} + 130 x^{9} + 2639 x^{8} - 20579 x^{7} - 202852 x^{6} - 634751 x^{5} - 1472133 x^{4} - 1620554 x^{3} - 2339103 x^{2} - 3891030 x - 3741300$	$13$	[1,6]	$3^{6}\cdot 13^{24}$	$2$	$189.11266470488542$	$197.27471817203326$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$49220254401.852295$
13.1.673...625.1	$x^{13} - 3 x^{12} - 87 x^{11} + 736 x^{10} - 1956 x^{9} - 15927 x^{8} + 216019 x^{7} - 1196967 x^{6} + 4265724 x^{5} - 10045872 x^{4} + 13521123 x^{3} - 7227009 x^{2} + 1336176 x + 150417$	$13$	[1,6]	$3^{6}\cdot 5^{6}\cdot 79^{12}$	$3$	$197.0004085878747$	$218.62579719842265$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$22619543081.392696$
13.1.918...696.1	$x^{13} - 3 x^{12} - 20 x^{11} - 442 x^{10} - 1158 x^{9} - 8910 x^{8} - 28900 x^{7} - 87096 x^{6} - 235075 x^{5} - 683399 x^{4} - 310920 x^{3} - 4432014 x^{2} + 2317896 x - 9303336$	$13$	[1,6]	$2^{12}\cdot 157^{12}$	$2$	$201.7707167217356$	$212.82090722547485$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$111104186554.76862$
13.1.201...000.1	$x^{13} - 5 x^{12} + 89 x^{11} - 169 x^{10} + 3157 x^{9} + 2511 x^{8} + 85351 x^{7} + 44569 x^{6} + 2281802 x^{5} + 2145374 x^{4} + 21429280 x^{3} + 30773160 x^{2} + 296366400 x - 256176000$	$13$	[1,6]	$2^{18}\cdot 5^{6}\cdot 53^{12}$	$3$	$214.31450621191883$	$246.98425022800217$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$520185593593.02435$
13.1.222...656.1	$x^{13} - 65 x^{11} - 234 x^{10} + 2496 x^{9} + 20384 x^{8} - 29198 x^{7} - 617916 x^{6} - 805779 x^{5} + 8972912 x^{4} + 36211279 x^{3} + 69402918 x^{2} + 149865170 x + 312443504$	$13$	[1,6]	$2^{12}\cdot 13^{24}$	$2$	$215.96563291237553$	$227.7932232818619$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$207936088101.1773$
13.1.310...409.1	$x^{13} - 2 x^{12} + 10 x^{11} + 258 x^{10} - 3479 x^{9} + 33282 x^{8} - 239440 x^{7} + 1280804 x^{6} - 5604449 x^{5} + 19580056 x^{4} - 54615776 x^{3} + 123896384 x^{2} - 186790400 x + 217296896$	$13$	[1,6]	$43^{6}\cdot 53^{12}$	$2$	$221.58878806406514$	$256.0787210024293$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$27433358551.359776$
13.1.529...889.1	$x^{13} - 6 x^{12} + 37 x^{11} - 931 x^{10} + 6786 x^{9} + 7676 x^{8} - 239053 x^{7} + 775209 x^{6} + 575926 x^{5} - 9699404 x^{4} + 39903362 x^{3} - 121704691 x^{2} + 219063750 x - 153159823$	$13$	[1,6]	$47^{6}\cdot 53^{12}$	$2$	$230.87490893108227$	$267.72454750416307$	?	$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$1272245986.042585$
13.1.669...384.1	$x^{13} - 4 x^{12} - 43 x^{11} - 630 x^{10} + 3024 x^{9} + 41140 x^{8} + 52458 x^{7} - 148068 x^{6} - 142751 x^{5} - 9384148 x^{4} - 39792623 x^{3} - 54086038 x^{2} - 17702658 x - 1723756$	$13$	[1,6]	$2^{18}\cdot 131^{12}$	$2$	$235.07965037870517$	$254.6532753300448$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$274109732012.39703$
13.1.971...624.1	$x^{13} - 3 x^{12} + 102 x^{11} - 918 x^{10} + 4737 x^{9} - 24531 x^{8} + 91500 x^{7} - 409320 x^{6} + 1438464 x^{5} - 2679528 x^{4} + 3981072 x^{3} + 15360192 x^{2} - 5038928 x + 2129616$	$13$	[1,6]	$2^{12}\cdot 13^{6}\cdot 53^{12}$	$3$	$241.90275107189012$	$281.60537249650423$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$610629639673.7336$
13.1.207...881.1	$x^{13} - x^{12} - 24 x^{11} - 34 x^{10} - 764 x^{9} - 3402 x^{8} + 122677 x^{7} - 1291 x^{6} - 2450194 x^{5} - 2224784 x^{4} + 24924920 x^{3} - 45391040 x^{2} + 155652000 x - 301007936$	$13$	[1,6]	$53^{12}\cdot 59^{6}$	$2$	$256.4221736507937$	$299.96132966520094$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$22206481899.068287$
13.1.485...984.1	$x^{13} - 2 x^{12} + 169 x^{11} - 1120 x^{10} + 11149 x^{9} - 84590 x^{8} + 440179 x^{7} - 1643948 x^{6} + 4209826 x^{5} - 7753316 x^{4} + 7867196 x^{3} + 1215376 x^{2} + 361080 x - 17537200$	$13$	[1,6]	$2^{12}\cdot 17^{6}\cdot 53^{12}$	$3$	$273.78686479326643$	$322.0280636267129$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$478241843781.621$
13.13.123...449.1	$x^{13} - 3 x^{12} - 278 x^{11} + 205 x^{10} + 24414 x^{9} + 55909 x^{8} - 638959 x^{7} - 3888668 x^{6} - 8795208 x^{5} - 9304040 x^{4} - 4272496 x^{3} - 446336 x^{2} + 199680 x + 41600$	$13$	[13,0]	$13^{6}\cdot 131^{12}$	$2$	$294.1250228866634$	$324.62050502705364$		$D_{13}$ (as 13T2)	$[13]$	$2$	$12$	$1357845156620.764$
13.1.207...601.1	$x^{13} - x^{12} - 36 x^{11} - 397 x^{10} - 1373 x^{9} - 7908 x^{8} - 19340 x^{7} - 141952 x^{6} - 314331 x^{5} - 1370643 x^{4} - 926037 x^{3} - 2851884 x^{2} + 4802031 x - 2755701$	$13$	[1,6]	$3^{6}\cdot 13^{6}\cdot 79^{12}$	$3$	$306.1916108114179$	$352.52350548818606$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$135872992988.97057$
13.1.397...161.1	$x^{13} - 5 x^{12} + 84 x^{11} - 1302 x^{10} + 11783 x^{9} - 73711 x^{8} + 187812 x^{7} + 1504262 x^{6} - 18024087 x^{5} + 85600943 x^{4} - 201263250 x^{3} + 194089064 x^{2} + 92994360 x + 57084208$	$13$	[1,6]	$11^{6}\cdot 157^{12}$	$2$	$321.8304053902648$	$352.92354840496824$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$132354354281.5214$
13.1.644...449.1	$x^{13} - 3 x^{12} - 44 x^{11} - 35 x^{10} + 2464 x^{9} - 1115 x^{8} - 23469 x^{7} - 156068 x^{6} - 1328832 x^{5} + 7506120 x^{4} + 4428000 x^{3} + 149886720 x^{2} + 1110661632 x - 10899339264$	$13$	[1,6]	$3^{6}\cdot 313^{12}$	$2$	$334.03286489919657$	$348.44963654876545$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$2127268579399.9524$
13.1.362...376.1	$x^{13} - 6 x^{12} - 176 x^{11} + 346 x^{10} + 3742 x^{9} + 32554 x^{8} + 598840 x^{7} + 1158934 x^{6} + 13216353 x^{5} + 10594924 x^{4} + 81511464 x^{3} + 59954112 x^{2} + 43334352 x - 6391872$	$13$	[1,6]	$2^{12}\cdot 313^{12}$	$2$	$381.4637120896399$	$402.354982920914$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$7450110001302.259$
13.1.105...481.1	$x^{13} - 5 x^{12} + 84 x^{11} - 988 x^{10} + 9742 x^{9} - 8870 x^{8} + 53263 x^{7} + 5084647 x^{6} - 25221438 x^{5} + 171040500 x^{4} + 318624352 x^{3} - 4101623104 x^{2} + 25376391168 x - 56568738816$	$13$	[1,6]	$19^{6}\cdot 157^{12}$	$2$	$414.16964352397105$	$463.832413834245$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$1180221156967.2769$
13.1.803...929.1	$x^{13} - 78 x^{11} - 741 x^{10} + 12558 x^{9} - 205244 x^{8} + 1537094 x^{7} - 7661940 x^{6} + 59719647 x^{5} - 105143662 x^{4} + 907756590 x^{3} - 1195524525 x^{2} + 4136164500 x - 9214480625$	$13$	[1,6]	$13^{24}\cdot 23^{6}$	$2$	$484.173008319412$	$546.2289605060831$	?	$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$277763963323.49176$
13.1.231...064.1	$x^{13} - 6 x^{12} - 176 x^{11} + 972 x^{10} + 19079 x^{9} - 36306 x^{8} - 783368 x^{7} + 9665648 x^{6} + 6090908 x^{5} - 447853672 x^{4} - 90200336 x^{3} + 6112031968 x^{2} + 5407358080 x + 37248420608$	$13$	[1,6]	$2^{18}\cdot 313^{12}$	$2$	$525.2791368350838$	$569.0158737351516$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$25714057531861.82$
13.1.156...041.1	$x^{13} - 5 x^{12} - 157 x^{11} + 3849 x^{10} - 27501 x^{9} - 181329 x^{8} + 5156944 x^{7} - 48686796 x^{6} + 211658672 x^{5} - 52353024 x^{4} - 3852444928 x^{3} + 15773175808 x^{2} + 7360458752 x - 130877702144$	$13$	[1,6]	$11^{6}\cdot 313^{12}$	$2$	$608.4461764230781$	$667.2302554392634$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$8565152375022.607$
13.1.163...536.1	$x^{13} - 5 x^{12} + 252 x^{11} + 366 x^{10} + 18364 x^{9} + 152724 x^{8} + 1072048 x^{7} + 6272184 x^{6} + 51218016 x^{5} + 201573536 x^{4} - 382598144 x^{3} - 1230343680 x^{2} + 6659260416 x + 22658973696$	$13$	[1,6]	$2^{12}\cdot 521^{12}$	$2$	$610.5539542226127$	$643.99159877574$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$181822102788808.88$
13.1.333...449.1	$x^{13} - 4 x^{12} - 353 x^{11} + 2032 x^{10} + 3194 x^{9} - 346412 x^{8} + 8212739 x^{7} + 2289760 x^{6} - 119737150 x^{5} - 1998689236 x^{4} - 21857523353 x^{3} + 378346808648 x^{2} + 3681955643997 x + 7513203573312$	$13$	[1,6]	$3^{6}\cdot 937^{12}$	$2$	$919.0815491916796$	$958.7488700285892$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$1524359865500224.2$
13.1.187...376.1	$x^{13} - x^{12} - 432 x^{11} + 2140 x^{10} + 106911 x^{9} - 1102415 x^{8} - 10059196 x^{7} + 178713544 x^{6} + 620853524 x^{5} - 23529732460 x^{4} + 94864494208 x^{3} + 607423562464 x^{2} - 4817926273344 x + 9294819625792$	$13$	[1,6]	$2^{12}\cdot 937^{12}$	$2$	$1049.5861225318563$	$1107.067836392511$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$4767150164934258.0$
13.1.211...129.1	$x^{13} - 3 x^{12} - 164 x^{11} - 1795 x^{10} - 50966 x^{9} + 707255 x^{8} + 13406544 x^{7} + 99172559 x^{6} - 2922109971 x^{5} - 27431219976 x^{4} + 442607350140 x^{3} - 602751131928 x^{2} - 2438359227648 x - 17721860853600$	$13$	[1,6]	$3^{6}\cdot 1093^{12}$	$2$	$1059.473160753311$	$1105.1997470640229$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$4072873637937157.5$
13.1.105...729.1	$x^{13} - 3 x^{12} - 188 x^{11} - 2435 x^{10} + 35368 x^{9} + 1048861 x^{8} - 22054750 x^{7} + 66087355 x^{6} + 3077523728 x^{5} - 55471208845 x^{4} + 476449451660 x^{3} - 2491236180397 x^{2} + 7175069189745 x - 8475755343400$	$13$	[1,6]	$3^{6}\cdot 1249^{12}$	$2$	$1198.32642857353$	$1250.0458858419083$		$D_{13}$ (as 13T2)	$[13]$	$2$	$6$	$16708492997394952$

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Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.