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Curves (147)

curve a-invariants rank torsion log N log |Δ| Faltings height naive height
#1992 [1, 0, 0, -1779353550079…, 34258366504667…] ≥ 20 ℤ/2ℤ 208.23 367.66 29.32 375.19
#1996 [1, -1, 1, -5598400084645…, 44651244271983…] ≥ 19 ℤ/2ℤ 193.19 339.44 27.01 348.35
#1997 [1, 0, 1, -2473171297950…, 47340055711440…] ≥ 18 ℤ/2ℤ 191.25 305.00 24.68 325.18
#1998 [1, 0, 0, -5450464199885…, -7985404066455…] ≥ 18 ℤ/2ℤ 196.97 333.60 26.50 341.37
#3485 [1, 0, 0, -5384108389823…, 15204073247883…] ≥ 17 ℤ/2ℤ 146.35 256.58 20.39 272.25
#3472 [1, 1, 1, -9040157640002…, 71844692098536…] ≥ 17 ℤ/2ℤ 150.36 272.62 21.42 280.71
#2146 [1, -1, 1, -1018436625192…, 58853455947619…] ≥ 17 ℤ/2ℤ 168.69 273.37 21.48 281.07
#2160 [1, -1, 1, -1376287698021…, 62114650230038…] ≥ 17 ℤ/2ℤ 168.69 274.52 21.82 288.88
#2000 [1, 0, 0, -7010823537213…, 10033288229518…] ≥ 17 ℤ/2ℤ 151.24 286.28 22.56 294.45
#1999 [1, 0, 0, -1607547610816…, 76377482560170…] ≥ 17 ℤ/2ℤ 163.85 292.75 23.17 303.16
#3488 [1, -1, 1, -1433531895173…, 31941409442865…] ≥ 16 ℤ/2ℤ 137.98 233.17 18.12 240.65
#3487 [1, -1, 1, -1978662656511…, 19547913950717…] ≥ 16 ℤ/2ℤ 133.71 233.76 18.18 241.62
#3489 [1, 0, 0, -2653537278084…, 52377999300372…] ≥ 16 ℤ/2ℤ 135.23 230.32 18.04 242.50
#2001 [1, 0, 0, -2402337110502…, 51657476116291…] ≥ 16 ℤ/2ℤ 139.10 241.51 18.82 249.11
#2147 [1, 0, 0, -5434530300889…, 48746430388378…] ≥ 16 ℤ/2ℤ 137.33 236.81 18.70 251.56
#2002 [1, 0, 0, -3221870882255…, 69750098909627…] ≥ 16 ℤ/2ℤ 141.34 245.43 19.27 256.89
#3471 [1, 0, 1, -3501180341006…, 79718109217596…] ≥ 16 ℤ/2ℤ 135.05 242.13 19.16 257.14
#3486 [1, 1, 1, -3575852680171…, 78511122853996…] ≥ 16 ℤ/2ℤ 132.27 247.35 19.37 257.21
#2159 [1, 0, 0, -8694423726071…, 31203931535373…] ≥ 16 ℤ/2ℤ 137.33 230.39 19.05 259.87
#2003 [1, -1, 0, 86172091259736…, 64868313631144…] ≥ 15 ℤ/2ℤ 101.03 175.60 13.31 183.05
#2004 [1, 0, 0, -8836282290513…, 14376898779874…] ≥ 15 ℤ/2ℤ 117.06 204.13 15.71 212.27
#2315 [0, 1, 0, -1638845978843…, 57340415418471…] ≥ 14 ℤ/2ℤ 92.35 156.91 11.78 165.07
#2005 [1, 0, 0, -9959584832935…, 37752078253065…] ≥ 14 ℤ/2ℤ 100.40 166.29 12.66 177.39
#2006 [1, 0, 0, -9739872505237…, 36997549385777…] ≥ 14 ℤ/2ℤ 102.13 186.83 14.71 204.95
#2007 [0, 1, 0, -1917477672479…, -1125424112540…] ≥ 14 ℤ/2ℤ 133.06 206.31 15.88 213.89
#3547 [1, 0, 0, -1292137673238…, 56490525161322…] ≥ 13 ℤ/2ℤ 82.36 136.61 10.31 150.54
#3548 [1, 0, 0, -1001111084356…, 82620906840913…] ≥ 13 ℤ/2ℤ 82.36 143.60 10.66 151.30
#3009 [0, 0, 0, -6497783767474…, 63751249522807…] ≥ 13 ℤ/2ℤ 89.81 137.63 10.59 155.38
#2161 [0, -1, 0, -2325124713051…, 85689370890651…] ≥ 13 ℤ/2ℤ 92.59 148.49 11.06 155.97
#2162 [0, -1, 0, -7865618818149…, 26734145448848…] ≥ 13 ℤ/2ℤ 92.59 150.66 11.40 162.86
#2163 [0, 1, 0, -1679193857764…, 16079645324828…] ≥ 13 ℤ/2ℤ 95.49 163.59 12.31 171.05
#2165 [0, 1, 0, -1063298052122…, 41828967045778…] ≥ 13 ℤ/2ℤ 95.49 166.09 12.66 177.58
#2164 [1, 1, 1, -7308940636813…, 76053858405569…] ≥ 13 ℤ/2ℤ 99.07 165.77 12.93 183.37
#2008 [0, 0, 0, -1940028278154…, 10307498134844…] ≥ 13 ℤ/2ℤ 103.38 181.72 13.96 193.20
#2009 [1, -1, 1, -8003670699920…, 86885027474371…] ≥ 13 ℤ/2ℤ 102.12 184.91 14.27 197.45
#2012 [1, 0, 0, -1943384300833…, 32972855024330…] ≥ 13 ℤ/2ℤ 112.60 183.76 14.36 200.12
#2011 [0, 0, 0, -1083034930847…, 42926501459585…] ≥ 13 ℤ/2ℤ 102.76 193.95 14.97 205.27
#1993 [1, -1, 1, -2020050562772…, 77043916201717…] ≥ 13 ℤ/2ℤ × ℤ/2ℤ 145.94 392.44 31.41 400.56
#2010 [0, 1, 0, -1622134663627…, -1709160933239…] ≥ 13 ℤ/2ℤ × ℤ/2ℤ 157.83 398.73 31.93 406.81
#2013 [0, 1, 0, 40464077808839…, 11170507920941…] ≥ 12 ℤ/2ℤ 70.25 126.60 9.24 133.48
#2014 [1, 0, 1, -5794953730320…, -1083260730728…] ≥ 12 ℤ/2ℤ 78.58 126.86 9.26 134.32
#2019 [0, 1, 0, -1252663771253…, 22042752770562…] ≥ 11 ℤ/2ℤ 82.27 128.99 9.44 136.63
#2020 [0, 1, 0, 33988095895545…, 21174748052513…] ≥ 11 ℤ/2ℤ 94.87 146.56 10.90 153.44
#2087 [0, 1, 0, -4409617792349…, -1312725369424…] ≥ 11 ℤ/2ℤ 79.14 160.58 12.07 168.04
#2088 [0, 1, 0, -2692576074865…, 24460666158778…] ≥ 11 ℤ/2ℤ 79.14 168.99 12.76 176.49
#2017 [1, 1, 1, -6417061776794…, 19785732211482…] ≥ 11 ℤ/2ℤ 85.09 182.81 14.54 203.70
#2015 [1, 1, 1, -1634335456255…, -4263958956315…] ≥ 11 ℤ/2ℤ × ℤ/2ℤ 96.05 240.49 18.73 247.95
#2016 [0, -1, 0, -2979702126501…, 19797146077964…] ≥ 11 ℤ/2ℤ × ℤ/2ℤ 91.34 231.58 18.44 249.75
#2018 [0, 1, 0, -5412871027899…, 48471854131582…] ≥ 11 ℤ/2ℤ 88.23 207.00 18.14 251.54
#2021 [0, -1, 0, -3032742853505, 15413520131227…] ≥ 10 ℤ/2ℤ 51.06 90.37 6.22 97.84
#2090 [1, 1, 1, 11932381692979…, -1979842001406…] ≥ 10 ℤ/2ℤ 60.88 136.88 10.09 143.83
#2089 [1, 1, 1, -7238567263488…, -2370220075388…] ≥ 10 ℤ/2ℤ 60.88 132.70 10.09 148.80
#2091 [0, 0, 0, -8432841741464…, -3938366605811…] ≥ 10 ℤ/2ℤ 66.58 162.33 12.22 169.98
#2023 [0, 0, 0, -7009893429627…, 22589944527336…] ≥ 10 ℤ/2ℤ 66.58 153.97 12.22 176.33
#2025 [0, 1, 0, -3012444009560…, 20124296924202…] ≥ 10 ℤ/2ℤ 70.62 162.74 12.70 180.71
#2022 [0, 1, 0, -4181221879740…, 29795568333639…] ≥ 10 ℤ/2ℤ × ℤ/2ℤ 69.33 172.52 13.11 181.69
#2024 [1, 1, 1, -2215240130539…, 44669500441213…] ≥ 10 ℤ/2ℤ × ℤ/2ℤ 70.63 186.01 14.19 193.60
#2027 [0, -1, 0, 3090014805, 27966726311676] ≥ 9 ℤ/2ℤ 47.26 69.88 4.51 77.17
#2028 [0, -1, 0, 6016054524, 11625772485747…] ≥ 9 ℤ/2ℤ 49.39 72.06 4.69 79.17
#2094 [0, 1, 0, 12324101424, 21149652073354…] ≥ 9 ℤ/2ℤ 48.63 74.01 4.86 81.32
#2026 [0, -1, 0, 32630276060, 21913519124454…] ≥ 9 ℤ/2ℤ 48.79 77.44 5.14 84.24
#2029 [0, -1, 0, -38802409025, 65116761573459…] ≥ 9 ℤ/2ℤ 43.24 78.66 5.24 86.35
#2095 [1, 1, 1, -1172358580750…, 15161392242705…] ≥ 9 ℤ/2ℤ × ℤ/2ℤ 64.12 160.22 12.14 170.97
#2030 [1, 0, 1, -1420833844172…, 47101528298497…] ≥ 9 ℤ/2ℤ × ℤ/2ℤ 66.84 164.04 12.36 171.55
#2031 [1, -1, 1, -1262226950286…, 17129189830354…] ≥ 9 ℤ/2ℤ × ℤ/2ℤ 60.86 173.36 13.27 185.01
#2032 [1, 0, 0, -2379992149449…, 44542952883353…] ≥ 9 ℤ/6ℤ 69.84 215.88 16.85 228.36
#2098 [1, 0, 0, -7967320834038…, 26976176262494…] ≥ 9 ℤ/4ℤ 73.16 220.98 17.21 231.98
#2099 [1, 0, 0, 55634371339019…, -2765121350121…] ≥ 9 ℤ/4ℤ 73.16 230.62 17.91 237.81
#2033 [1, 0, 0, -2169804093800…, -3888327340812…] ≥ 9 ℤ/2ℤ × ℤ/2ℤ 73.16 227.53 17.91 241.89
#2103 [0, 1, 0, -6128849579934…, 58817774891634…] ≥ 9 ℤ/4ℤ 79.14 254.03 20.00 265.75
#2096 [0, 1, 0, -9825609019887…, 37487573620515…] ≥ 9 ℤ/4ℤ 79.14 227.23 20.00 274.06
#2097 [1, 0, 0, -1352161593194…, 60514755240142…] ≥ 9 ℤ/4ℤ 87.09 286.29 22.90 302.64
#2092 [1, 0, 0, -1805673781082…, 93354844841698…] ≥ 9 ℤ/6ℤ 89.64 288.91 23.03 303.51
#2102 [1, 0, 0, 33112058816367…, 32163354268157…] ≥ 9 ℤ/4ℤ 87.09 298.95 23.60 305.99
#2034 [0, 1, 0, -2056755905, 27106485989599] ≥ 8 ℤ/2ℤ 36.44 67.65 4.35 75.95
#2104 [0, -1, 0, -1153759435792…, -9965707448092…] ≥ 8 ℤ/2ℤ × ℤ/2ℤ 48.76 122.02 8.86 129.47
#2106 [1, 0, 0, -6507086270485…, 19660598017457…] ≥ 8 ℤ/2ℤ × ℤ/2ℤ 46.90 138.09 10.28 148.48
#2105 [1, 0, 0, -6873429016852…, -5703731609378…] ≥ 8 ℤ/2ℤ × ℤ/2ℤ 49.58 141.12 10.45 148.64
#1995 [1, 0, 1, -5341863310003…, -1480889838723…] ≥ 8 ℤ/6ℤ 56.81 178.34 13.66 189.33
#2109 [0, 1, 0, -1682495173614…, 22297117299299…] ≥ 8 ℤ/4ℤ 62.29 200.94 15.43 208.54
#2110 [1, 0, 0, -6565609812540…, 20476735373202…] ≥ 8 ℤ/4ℤ 62.42 183.28 15.45 217.58
#2111 [1, 0, 0, -6863149950567…, 18519194349292…] ≥ 8 ℤ/2ℤ × ℤ/2ℤ 62.42 209.00 16.14 217.72
#2112 [1, 0, 0, -6269077543829…, 22410072741352…] ≥ 8 ℤ/4ℤ 62.42 209.01 16.14 217.76
#2107 [1, 0, 0, -1404214413958…, -1884486552632…] ≥ 8 ℤ/6ℤ 62.45 217.31 16.85 226.77
#2108 [1, 0, 0, -7608879975600…, 25546370930384…] ≥ 8 ℤ/6ℤ 68.17 214.99 17.84 245.66
#2035 [0, 1, 0, -2947665298556…, 22183025450436…] ≥ 7 ℤ/2ℤ × ℤ/2ℤ 48.52 152.33 11.39 159.92
#2036 [1, 0, 1, -6444802130025…, 19912528816122…] ≥ 7 ℤ/6ℤ 46.39 146.11 11.21 162.27
#2037 [1, 1, 0, -309383, -57492993] ≥ 6 ℤ/2ℤ 25.71 40.70 2.12 49.54
#2039 [1, 1, 0, -33616172125, 23712619964781…] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 29.90 69.82 4.77 84.33
#2038 [1, -1, 1, -102379814996, 12509767707233…] ≥ 6 ℤ/2ℤ × ℤ/2ℤ 31.14 76.06 5.16 87.67
#2040 [1, 0, 1, -2580444998885…, 46144993235639…] ≥ 6 ℤ/6ℤ 42.67 136.44 10.11 145.70
#2041 [1, 1, 1, -2797287263082…, -2695185857636…] ≥ 6 ℤ/2ℤ × ℤ/4ℤ 60.46 255.90 20.02 263.38
#2042 [0, -1, 0, 15935, 3256321] ≥ 5 ℤ/2ℤ 19.26 36.12 1.69 43.52
#2044 [0, 0, 0, -133250061, 442464394660] ≥ 5 ℤ/2ℤ × ℤ/2ℤ 25.16 59.46 3.66 67.74
#2043 [1, 1, 1, -494007199, -1140782678404] ≥ 5 ℤ/2ℤ × ℤ/2ℤ 23.89 64.14 4.04 71.67
#2045 [1, 0, 1, -803641707349, 71375888363434…] ≥ 5 ℤ/6ℤ 29.53 88.12 6.03 95.74
#2046 [1, 0, 0, -3507823901554…, 25287433007393…] ≥ 5 ℤ/6ℤ 29.32 89.07 6.85 112.09
#2047 [1, 0, 0, -2078158957197…, -1125593515635…] ≥ 5 ℤ/2ℤ × ℤ/4ℤ 46.06 182.90 14.02 193.41
#2049 [0, 0, 0, -436341, -57965780] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 18.64 42.80 2.26 50.57
#2051 [1, -1, 1, -837356, -213199594] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 18.02 44.33 2.40 52.53
#2053 [0, -1, 0, -947508, -45367488] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 18.40 45.43 2.48 52.90
#2048 [0, -1, 0, -1500854, 706937784] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 18.94 41.20 2.32 54.28
#2050 [0, 0, 0, -1891731, 989132690] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 18.32 43.81 2.46 54.97
#2052 [1, 1, 1, -3156938, 2149966406] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 17.74 44.11 2.53 56.51
#2054 [0, -1, 0, -15483302840, 26574437157750…] ≥ 4 ℤ/2ℤ × ℤ/2ℤ 22.55 74.41 4.89 82.00
#2055 [0, 1, 0, -9630104529315…, 11502552305812…] ≥ 4 ℤ/2ℤ × ℤ/4ℤ 29.64 108.27 8.31 128.93
#2144 [1, 0, 0, -1435365919737…, 21086903195077…] ≥ 4 ℤ/7ℤ 29.91 118.47 8.70 130.14
#2121 [1, 0, 0, 10303505179101…, 10900516450869…] ≥ 4 ℤ/7ℤ 31.35 128.66 9.41 136.04
#1994 [1, 0, 0, 68482128318557…, 44571609691519…] ≥ 4 ℤ/10ℤ 50.24 239.53 18.64 246.77
#2138 [1, 0, 0, -9701467799711…, 36779369791425…] ≥ 4 ℤ/10ℤ 53.48 239.96 21.13 287.83
#2056 [1, 1, 0, 168, 210] ≥ 3 ℤ/2ℤ 11.64 19.55 0.32 26.98
#2113 [0, -1, 0, -1454, 14784] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 14.09 25.41 0.82 33.46
#2114 [0, -1, 0, -1849, 1849] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 13.36 26.73 0.92 34.18
#2057 [1, 0, 0, -3809, 56784] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 13.09 28.39 1.07 36.35
#2058 [0, 0, 0, -317611, -49080870] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 12.29 41.46 2.16 49.62
#2059 [0, -1, 0, -2347904, 1378488384] ≥ 3 ℤ/2ℤ × ℤ/2ℤ 13.90 43.57 2.47 55.62
#2172 [0, -1, 0, -10428240, 9127296000] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 16.51 51.95 3.04 60.09
#2060 [1, 1, 1, -125088518240, -2591233519185…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 20.47 80.79 5.42 88.27
#2061 [1, 0, 0, -3072505791404, 17006233003330…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 20.32 89.30 6.16 97.87
#2062 [1, 0, 0, -1957385103361…, 11455664232096…] ≥ 3 ℤ/2ℤ × ℤ/4ℤ 27.56 137.30 10.13 144.88
#2115 [1, 0, 0, -9267795625566…, 29941809054114…] ≥ 3 ℤ/10ℤ 32.32 140.66 10.45 149.54
#2117 [1, 0, 0, 14915200199076…, 16005999857796…] ≥ 3 ℤ/10ℤ 32.32 145.34 10.79 152.62
#2116 [1, 0, 0, -2558452512972…, 16560261648275…] ≥ 3 ℤ/10ℤ 31.92 142.88 10.66 152.69
#2120 [1, 0, 0, -1139407008286…, 42920697550927…] ≥ 3 ℤ/10ℤ 33.84 149.53 11.15 157.07
#2119 [1, 0, 0, -3338488361636…, 23118493712440…] ≥ 3 ℤ/10ℤ 32.20 150.49 11.22 157.96
#2118 [1, 0, 0, -6666890136604…, 66257197320818…] ≥ 3 ℤ/10ℤ 33.63 135.89 11.43 169.28
#2063 [1, 1, 1, -26, 38] ≥ 2 ℤ/2ℤ 8.11 11.40 -0.29 21.39
#2064 [0, -1, 0, -884, 10404] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 8.58 18.54 0.45 31.97
#2066 [1, 0, 0, -31464, -1542321] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 9.60 34.51 1.58 42.68
#2065 [0, 1, 0, -38344, -2700544] ≥ 2 ℤ/2ℤ × ℤ/2ℤ 10.63 33.82 1.56 43.28
#2067 [1, 0, 0, -6076154, 5652540579] ≥ 2 ℤ/2ℤ × ℤ/4ℤ 13.13 47.76 2.77 58.47
#2069 [1, 0, 0, -8735254, 9914033444] ≥ 2 ℤ/2ℤ × ℤ/4ℤ 12.44 46.70 2.77 59.56
#2068 [1, 1, 1, -15333290, 22065838247] ≥ 2 ℤ/2ℤ × ℤ/4ℤ 12.64 51.36 3.04 61.25
#2173 [1, 0, 1, -244941793, 318865017056] ≥ 2 ℤ/2ℤ × ℤ/6ℤ 15.69 62.06 3.86 69.56
#2070 [1, 0, 0, -3736334241305, 27798198052544…] ≥ 2 ℤ/2ℤ × ℤ/6ℤ 17.42 69.69 5.61 98.46
#2071 [1, 0, 0, -6270194200626…, -7706664118858…] ≥ 2 ℤ/2ℤ × ℤ/4ℤ 18.95 99.29 6.97 106.92
#2124 [1, 0, 0, -3862230018500…, 91420337087883…] ≥ 2 ℤ/2ℤ × ℤ/4ℤ 19.53 107.96 7.81 119.28
#2136 [0, 1, 1, 13, 42] ≥ 1 ℤ/3ℤ 4.51 13.53 -0.19 20.80
#2073 [1, -1, 1, -27, 26] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 5.32 13.86 -0.15 21.47
#2072 [0, -1, 0, -56, 180] ≥ 1 ℤ/2ℤ 6.17 12.24 -0.16 23.71
#2076 [0, -1, 0, -64, 64] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 5.82 16.60 0.07 24.11
#2075 [1, 0, 0, -474, 2619] ≥ 1 ℤ/2ℤ × ℤ/2ℤ 6.06 22.05 0.54 30.10
#2074 [1, -1, 1, -626, 6180] ≥ 1 ℤ/2ℤ 4.76 13.55 0.23 30.93
#2078 [1, 1, 1, -1154, 12431] ≥ 1 ℤ/2ℤ × ℤ/4ℤ 6.87 23.99 0.72 32.77
#2077 [1, 0, 0, -3910, 93347] ≥ 1 ℤ/2ℤ × ℤ/4ℤ 7.49 24.28 0.87 36.43
#2079 [1, 0, 1, -286534, 59011352] ≥ 1 ℤ/6ℤ 7.75 24.75 1.59 49.31
#2080 [1, 0, 0, -114223080, -283150929600] ≥ 1 ℤ/2ℤ × ℤ/4ℤ 11.32 59.37 3.65 67.27

Contributions to other curves (1)

curve a-invariants contribution rank when
#1498 [1, 0, 1, -999591626088641703, 349303002842534327752474006] improved rank ≥ 3 → ≥ 4 4