LMFDB - Number field search results

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Degree	Signature	Class number	Class group structure	CM field

Ramified prime count	Ramified	Unramified primes	Galois group	Galois

Discriminant	Root discriminant	Galois root discriminant	Regulator	Intermediate field

$p$-adic completions	Minimal sibling	Monogenic	Index	Ines. $p$

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Results (1-50 of 1776660 matches)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	Galois root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Regulator
2.0.5711.1	$x^{2} - x + 1428$	$2$	[0,1]	$-\,5711$	$1$	$75.5711585196$	$75.57115851963631$	✓	✓	✓	$C_2$ (as 2T1)	$[109]$	$2$	$1$
2.0.5759.1	$x^{2} - x + 1440$	$2$	[0,1]	$-\,13\cdot 443$	$2$	$75.8880754796$	$75.88807547961669$	✓	✓	✓	$C_2$ (as 2T1)	$[108]$	$2$	$1$
2.0.5879.1	$x^{2} - x + 1470$	$2$	[0,1]	$-\,5879$	$1$	$76.6746372668$	$76.67463726683029$	✓	✓	✓	$C_2$ (as 2T1)	$[101]$	$2$	$1$
2.0.6359.1	$x^{2} - x + 1590$	$2$	[0,1]	$-\,6359$	$1$	$79.7433382798$	$79.74333827975852$	✓	✓	✓	$C_2$ (as 2T1)	$[101]$	$2$	$1$
2.0.6431.1	$x^{2} - x + 1608$	$2$	[0,1]	$-\,59\cdot 109$	$2$	$80.1935159474$	$80.19351594736322$	✓	✓	✓	$C_2$ (as 2T1)	$[114]$	$2$	$1$
2.0.6551.1	$x^{2} - x + 1638$	$2$	[0,1]	$-\,6551$	$1$	$80.938248066$	$80.93824806604107$	✓	✓	✓	$C_2$ (as 2T1)	$[117]$	$2$	$1$
2.0.6599.1	$x^{2} - x + 1650$	$2$	[0,1]	$-\,6599$	$1$	$81.2342292387$	$81.23422923866515$	✓	✓	✓	$C_2$ (as 2T1)	$[109]$	$2$	$1$
2.0.6719.1	$x^{2} - x + 1680$	$2$	[0,1]	$-\,6719$	$1$	$81.9695065253$	$81.96950652529269$	✓	✓	✓	$C_2$ (as 2T1)	$[105]$	$2$	$1$
2.0.6839.1	$x^{2} - x + 1710$	$2$	[0,1]	$-\,7\cdot 977$	$2$	$82.6982466561$	$82.6982466561414$	✓	✓	✓	$C_2$ (as 2T1)	$[108]$	$2$	$1$
2.0.7031.1	$x^{2} - x + 1758$	$2$	[0,1]	$-\,79\cdot 89$	$2$	$83.851058431$	$83.85105843100611$	✓	✓	✓	$C_2$ (as 2T1)	$[108]$	$2$	$1$
2.0.7199.1	$x^{2} - x + 1800$	$2$	[0,1]	$-\,23\cdot 313$	$2$	$84.8469209813$	$84.84692098125895$	✓	✓	✓	$C_2$ (as 2T1)	$[114]$	$2$	$1$
2.0.7271.1	$x^{2} - x + 1818$	$2$	[0,1]	$-\,11\cdot 661$	$2$	$85.2701589069$	$85.27015890685323$	✓	✓	✓	$C_2$ (as 2T1)	$[116]$	$2$	$1$
2.0.7391.1	$x^{2} - x + 1848$	$2$	[0,1]	$-\,19\cdot 389$	$2$	$85.9709253178$	$85.9709253178073$	✓	✓	✓	$C_2$ (as 2T1)	$[120]$	$2$	$1$
2.0.7439.1	$x^{2} - x + 1860$	$2$	[0,1]	$-\,43\cdot 173$	$2$	$86.2496376804$	$86.24963768039841$	✓	✓	✓	$C_2$ (as 2T1)	$[116]$	$2$	$1$
2.0.7559.1	$x^{2} - x + 1890$	$2$	[0,1]	$-\,7559$	$1$	$86.9425097406$	$86.94250974063263$	✓	✓	✓	$C_2$ (as 2T1)	$[115]$	$2$	$1$
2.0.7631.1	$x^{2} - x + 1908$	$2$	[0,1]	$-\,13\cdot 587$	$2$	$87.355595127$	$87.35559512704381$	✓	✓	✓	$C_2$ (as 2T1)	$[106]$	$2$	$1$
2.0.7679.1	$x^{2} - x + 1920$	$2$	[0,1]	$-\,7\cdot 1097$	$2$	$87.6299035718$	$87.62990357178307$	✓	✓	✓	$C_2$ (as 2T1)	$[106]$	$2$	$1$
2.0.7751.1	$x^{2} - x + 1938$	$2$	[0,1]	$-\,23\cdot 337$	$2$	$88.0397637434$	$88.03976374343584$	✓	✓	✓	$C_2$ (as 2T1)	$[110]$	$2$	$1$
2.0.7871.1	$x^{2} - x + 1968$	$2$	[0,1]	$-\,17\cdot 463$	$2$	$88.7186564371$	$88.71865643707642$	✓	✓	✓	$C_2$ (as 2T1)	$[120]$	$2$	$1$
2.0.7895.1	$x^{2} - x + 1974$	$2$	[0,1]	$-\,5\cdot 1579$	$2$	$88.8538125237$	$88.85381252371785$	✓	✓	✓	$C_2$ (as 2T1)	$[112]$	$2$	$1$
2.0.8039.1	$x^{2} - x + 2010$	$2$	[0,1]	$-\,8039$	$1$	$89.6604706657$	$89.66047066572872$	✓	✓	✓	$C_2$ (as 2T1)	$[113]$	$2$	$1$
2.0.8111.1	$x^{2} - x + 2028$	$2$	[0,1]	$-\,8111$	$1$	$90.0610903776$	$90.06109037758759$	✓	✓	✓	$C_2$ (as 2T1)	$[121]$	$2$	$1$
2.0.8159.1	$x^{2} - x + 2040$	$2$	[0,1]	$-\,41\cdot 199$	$2$	$90.3271830625$	$90.32718306246464$	✓	✓	✓	$C_2$ (as 2T1)	$[106]$	$2$	$1$
2.0.8231.1	$x^{2} - x + 2058$	$2$	[0,1]	$-\,8231$	$1$	$90.7248587764$	$90.72485877641255$	✓	✓	✓	$C_2$ (as 2T1)	$[107]$	$2$	$1$
2.0.8279.1	$x^{2} - x + 2070$	$2$	[0,1]	$-\,17\cdot 487$	$2$	$90.9890103254$	$90.98901032542337$	✓	✓	✓	$C_2$ (as 2T1)	$[126]$	$2$	$1$
2.0.8351.1	$x^{2} - x + 2088$	$2$	[0,1]	$-\,7\cdot 1193$	$2$	$91.3838060052$	$91.38380600522173$	✓	✓	✓	$C_2$ (as 2T1)	$[118]$	$2$	$1$
2.0.8399.1	$x^{2} - x + 2100$	$2$	[0,1]	$-\,37\cdot 227$	$2$	$91.6460582895$	$91.64605828948673$	✓	✓	✓	$C_2$ (as 2T1)	$[134]$	$2$	$1$
2.0.8519.1	$x^{2} - x + 2130$	$2$	[0,1]	$-\,7\cdot 1217$	$2$	$92.2984290224$	$92.29842902238369$	✓	✓	✓	$C_2$ (as 2T1)	$[110]$	$2$	$1$
2.0.8615.1	$x^{2} - x + 2154$	$2$	[0,1]	$-\,5\cdot 1723$	$2$	$92.8170243005$	$92.81702430050211$	✓	✓	✓	$C_2$ (as 2T1)	$[118]$	$2$	$1$
2.0.8711.1	$x^{2} - x + 2178$	$2$	[0,1]	$-\,31\cdot 281$	$2$	$93.3327380933$	$93.33273809334$	✓	✓	✓	$C_2$ (as 2T1)	$[132]$	$2$	$1$
2.0.8735.1	$x^{2} - x + 2184$	$2$	[0,1]	$-\,5\cdot 1747$	$2$	$93.4612219051$	$93.46122190513026$	✓	✓	✓	$C_2$ (as 2T1)	$[106]$	$2$	$1$
2.0.8759.1	$x^{2} - x + 2190$	$2$	[0,1]	$-\,19\cdot 461$	$2$	$93.5895293289$	$93.58952932887311$	✓	✓	✓	$C_2$ (as 2T1)	$[108]$	$2$	$1$
2.0.8831.1	$x^{2} - x + 2208$	$2$	[0,1]	$-\,8831$	$1$	$93.9734004918$	$93.9734004918413$	✓	✓	✓	$C_2$ (as 2T1)	$[109]$	$2$	$1$
2.0.8879.1	$x^{2} - x + 2220$	$2$	[0,1]	$-\,13\cdot 683$	$2$	$94.2284458112$	$94.22844581123049$	✓	✓	✓	$C_2$ (as 2T1)	$[130]$	$2$	$1$
2.0.8951.1	$x^{2} - x + 2238$	$2$	[0,1]	$-\,8951$	$1$	$94.6097246587$	$94.60972465872628$	✓	✓	✓	$C_2$ (as 2T1)	$[135]$	$2$	$1$
2.0.9071.1	$x^{2} - x + 2268$	$2$	[0,1]	$-\,47\cdot 193$	$2$	$95.2417975471$	$95.24179754708538$	✓	✓	✓	$C_2$ (as 2T1)	$[138]$	$2$	$1$
2.0.9119.1	$x^{2} - x + 2280$	$2$	[0,1]	$-\,11\cdot 829$	$2$	$95.4934552731$	$95.4934552731233$	✓	✓	✓	$C_2$ (as 2T1)	$[124]$	$2$	$1$
2.0.9191.1	$x^{2} - x + 2298$	$2$	[0,1]	$-\,7\cdot 13\cdot 101$	$3$	$95.8697032435$	$95.86970324351692$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 62]$	$2$	$1$
2.0.9215.1	$x^{2} - x + 2304$	$2$	[0,1]	$-\,5\cdot 19\cdot 97$	$3$	$95.9947915254$	$95.99479152537391$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 58]$	$2$	$1$
2.0.9239.1	$x^{2} - x + 2310$	$2$	[0,1]	$-\,9239$	$1$	$96.11971702$	$96.11971701997463$	✓	✓	✓	$C_2$ (as 2T1)	$[139]$	$2$	$1$
2.0.9383.1	$x^{2} - x + 2346$	$2$	[0,1]	$-\,11\cdot 853$	$2$	$96.8658866681$	$96.86588666811448$	✓	✓	✓	$C_2$ (as 2T1)	$[102]$	$2$	$1$
2.0.9455.1	$x^{2} - x + 2364$	$2$	[0,1]	$-\,5\cdot 31\cdot 61$	$3$	$97.2368243003$	$97.23682430026189$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 60]$	$2$	$1$
2.0.9479.1	$x^{2} - x + 2370$	$2$	[0,1]	$-\,9479$	$1$	$97.3601561215$	$97.36015612148535$	✓	✓	✓	$C_2$ (as 2T1)	$[101]$	$2$	$1$
2.0.9551.1	$x^{2} - x + 2388$	$2$	[0,1]	$-\,9551$	$1$	$97.7292177396$	$97.72921773962995$	✓	✓	✓	$C_2$ (as 2T1)	$[129]$	$2$	$1$
2.0.9671.1	$x^{2} - x + 2418$	$2$	[0,1]	$-\,19\cdot 509$	$2$	$98.3412426198$	$98.34124261976763$	✓	✓	✓	$C_2$ (as 2T1)	$[126]$	$2$	$1$
2.0.9719.1	$x^{2} - x + 2430$	$2$	[0,1]	$-\,9719$	$1$	$98.5849887153$	$98.58498871532116$	✓	✓	✓	$C_2$ (as 2T1)	$[133]$	$2$	$1$
2.0.9743.1	$x^{2} - x + 2436$	$2$	[0,1]	$-\,9743$	$1$	$98.7066360484$	$98.70663604844408$	✓	✓	✓	$C_2$ (as 2T1)	$[105]$	$2$	$1$
2.0.9791.1	$x^{2} - x + 2448$	$2$	[0,1]	$-\,9791$	$1$	$98.9494820603$	$98.94948206029176$	✓	✓	✓	$C_2$ (as 2T1)	$[119]$	$2$	$1$
2.0.9831.1	$x^{2} - x + 2458$	$2$	[0,1]	$-\,3\cdot 29\cdot 113$	$3$	$99.151399385$	$99.15139938498095$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 54]$	$2$	$1$
2.0.9911.1	$x^{2} - x + 2478$	$2$	[0,1]	$-\,11\cdot 17\cdot 53$	$3$	$99.5540054443$	$99.55400544428134$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 68]$	$2$	$1$

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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.