Elliptic Curve Rank Leaderboard

← home

Curves with torsion ℤ/7ℤ

Click a column header to sort; click again to reverse. Curves missing a value (no primes of bad reduction supplied yet) sort last.

Download the database (JSON) ↓

showing 77 of 3920 curves
curve a-invariants rank torsion log N log |Δ| Faltings height naive height
#1214 [1, 0, 0, -3260345148508…, 12613980717746…] ≥ 6 ℤ/7ℤ 81.32 333.11 26.45 340.95
#1094 [1, 0, 0, -3871874529581…, 29324436958319…] ≥ 5 ℤ/7ℤ 40.43 160.65 12.69 181.46
#1907 [1, 0, 0, 17189192408099…, 14347563590500…] ≥ 5 ℤ/7ℤ 42.58 178.72 13.58 185.93
#1908 [1, 0, 0, -2989806201437…, 62923591421774…] ≥ 5 ℤ/7ℤ 43.23 181.48 14.37 201.41
#2850 [1, 0, 0, -2392473066782…, 45246626407933…] ≥ 5 ℤ/7ℤ 45.04 202.40 15.71 214.56
#2857 [1, 0, 0, -1644173544974…, 29144075820496…] ≥ 5 ℤ/7ℤ 47.14 190.92 14.64 199.87
#2841 [1, 0, 0, -3618055990993…, 26536056649244…] ≥ 5 ℤ/7ℤ 48.24 195.80 15.20 208.89
#2840 [1, -1, 1, -8199848398909…, 90396625573145…] ≥ 5 ℤ/7ℤ 49.57 196.16 15.33 211.34
#2839 [1, 0, 0, -1215144980111…, 16303853171210…] ≥ 5 ℤ/7ℤ 51.27 201.01 16.33 226.34
#2832 [1, 0, 0, -8016342698371…, 31571024748180…] ≥ 5 ℤ/7ℤ 51.39 209.54 16.19 218.45
#2825 [1, 0, 0, -1118184507209…, 14391914697117…] ≥ 5 ℤ/7ℤ 51.56 204.99 16.40 226.09
#1631 [1, -1, 1, -5385873752997…, 47148386493451…] ≥ 4 ℤ/7ℤ 29.80 130.32 9.65 141.00
#1213 [1, -1, 1, -3164639642154…, 21706985668269…] ≥ 4 ℤ/7ℤ 29.88 126.31 9.41 139.41
#2144 [1, 0, 0, -1435365919737…, 21086903195077…] ≥ 4 ℤ/7ℤ 29.91 118.47 8.70 130.14
#1626 [1, 0, 0, -7152365723323…, 22051381944801…] ≥ 4 ℤ/7ℤ 30.80 139.03 10.34 148.76
#1627 [1, 0, 0, 86546022235754…, 55483047848504…] ≥ 4 ℤ/7ℤ 30.81 129.50 9.48 136.68
#2121 [1, 0, 0, 10303505179101…, 10900516450869…] ≥ 4 ℤ/7ℤ 31.35 128.66 9.41 136.04
#1625 [1, 0, 0, 14511670805909…, 10109581236928…] ≥ 4 ℤ/7ℤ 35.40 150.54 11.23 157.79
#1629 [1, 0, 0, -1152089797356…, 51515479009752…] ≥ 4 ℤ/7ℤ 38.84 154.79 11.64 164.17
#1630 [1, -1, 1, -3414799361934…, 14607884665566…] ≥ 4 ℤ/7ℤ 38.96 173.18 13.13 181.08
#1628 [1, 0, 0, -1576164997076…, 24520713406861…] ≥ 4 ℤ/7ℤ 43.27 174.91 13.37 185.71
#1632 [1, 0, 0, -6582967677923…, 35903266972954…] ≥ 4 ℤ/7ℤ 50.64 197.04 15.11 204.89
#844 [1, 0, 0, -57339985560, 94379246762256…] ≥ 3 ℤ/7ℤ 19.81 79.26 5.30 87.09
#1560 [1, 0, 0, -2586270940000, 16035631383200…] ≥ 3 ℤ/7ℤ 20.34 84.20 5.91 97.36
#1562 [1, -1, 1, -8252027065587, 91198806819639…] ≥ 3 ℤ/7ℤ 20.60 86.39 6.15 100.84
#1555 [1, 0, 0, -6617482617830…, 21881550820093…] ≥ 3 ℤ/7ℤ 21.97 97.47 6.87 107.19
#1557 [1, 0, 0, -1186593208599…, 49626668168673…] ≥ 3 ℤ/7ℤ 22.38 109.90 8.03 122.65
#1558 [1, 0, 0, -4301779818679…, 98125192621178…] ≥ 3 ℤ/7ℤ 22.47 96.64 6.79 105.79
#1559 [1, -1, 1, -2590240406268…, 57038896693004…] ≥ 3 ℤ/7ℤ 22.60 95.48 6.69 104.50
#1561 [1, 0, 0, -700122879986, 26753064363877…] ≥ 3 ℤ/7ℤ 22.74 85.09 5.81 93.78
#1563 [1, -1, 1, 68236798429443, 23182400524040…] ≥ 3 ℤ/7ℤ 22.95 100.48 7.06 107.31
#1554 [1, -1, 1, -1259008791041…, 54379044724176…] ≥ 3 ℤ/7ℤ 23.14 92.97 6.78 109.01
#3384 [1, 0, 0, 41629871161444, -1168364015247…] ≥ 3 ℤ/7ℤ 23.27 99.06 6.94 105.94
#3370 [1, 0, 0, -1660228681553…, 38543763023078…] ≥ 3 ℤ/7ℤ 23.94 95.66 6.67 103.72
#3398 [1, 0, 0, -1378024147874…, 19689438735404…] ≥ 3 ℤ/7ℤ 24.85 92.36 7.18 116.19
#1187 [1, -1, 1, -15015087, 24405407799] ≥ 2 ℤ/7ℤ 13.15 52.06 3.08 61.36
#1464 [1, -1, 1, -97121697, 377834669169] ≥ 2 ℤ/7ℤ 13.61 56.37 3.48 66.84
#1465 [1, 0, 0, -3042724240, 68456442425600] ≥ 2 ℤ/7ℤ 13.65 67.57 4.38 77.24
#856 [1, 0, 0, -20945610, 70127864100] ≥ 2 ℤ/7ℤ 13.90 55.69 3.33 63.47
#855 [1, 0, 0, -10770571, 17614639217] ≥ 2 ℤ/7ℤ 14.53 52.34 3.07 60.71
#1459 [1, 0, 0, -151756056, 718674316992] ≥ 2 ℤ/7ℤ 14.56 54.65 3.46 68.13
#1460 [1, -1, 1, -86887443, 955765036083] ≥ 2 ℤ/7ℤ 15.21 61.13 3.78 68.69
#1461 [1, 0, 0, -164077875, 823376390625] ≥ 2 ℤ/7ℤ 15.32 57.58 3.59 68.40
#1462 [1, -1, 1, -3390568797, 78225013360869] ≥ 2 ℤ/7ℤ 15.39 67.17 4.37 77.50
#1463 [1, 0, 0, 1501735460, 75109915433960…] ≥ 2 ℤ/7ℤ 15.84 74.57 4.89 82.03
#3368 [1, 0, 0, -705036696, 7814059186752] ≥ 2 ℤ/7ℤ 16.02 63.54 4.04 72.90
#3369 [1, 0, 0, -2919020660, 60845521107600] ≥ 2 ℤ/7ℤ 16.41 64.19 4.22 77.00
#3397 [1, -1, 1, -317164020078, 68750282369702…] ≥ 2 ℤ/7ℤ 18.31 64.27 5.03 91.06
#1028 [1, -1, 1, -19353, 958713] ≥ 1 ℤ/7ℤ 6.35 31.89 1.40 41.23
#1769 [1, -1, 1, -5582262, 5077966149] ≥ 1 ℤ/7ℤ 8.46 40.43 2.49 58.22
#1750 [1, 0, 0, -1144386, 471132612] ≥ 1 ℤ/7ℤ 8.76 36.91 2.13 53.46
#1749 [1, -1, 1, -450273, 116420913] ≥ 1 ℤ/7ℤ 9.28 34.82 1.92 50.67
#1757 [1, 0, 0, 110624, 15558272] ≥ 1 ℤ/7ℤ 9.68 39.79 2.00 46.64
#1747 [1, 0, 0, -38760, 23169600] ≥ 1 ℤ/7ℤ 9.86 39.97 2.01 47.44
#1756 [1, 0, 0, -32311, 6205097] ≥ 1 ℤ/7ℤ 9.93 37.21 1.79 44.81
#1760 [1, 0, 0, 411779, 8250737] ≥ 1 ℤ/7ℤ 10.12 42.95 2.27 50.40
#1748 [1, 0, 0, -319040, 74649600] ≥ 1 ℤ/7ℤ 10.23 40.34 2.10 49.78
#1751 [1, 0, 0, -1330145, 291422025] ≥ 1 ℤ/7ℤ 10.38 46.18 2.54 53.92
#1767 [1, 0, 0, -2337511, 1374987977] ≥ 1 ℤ/7ℤ 10.65 40.64 2.36 55.61
#1758 [1, -1, 1, -137832, 20026539] ≥ 1 ℤ/7ℤ 10.67 36.16 1.81 47.14
#1761 [1, -1, 1, 621237, -226146597] ≥ 1 ℤ/7ℤ 11.13 45.07 2.44 52.00
#1759 [1, 0, 0, 430484, 453494672] ≥ 1 ℤ/7ℤ 11.15 45.99 2.51 53.39
#1768 [1, 0, 0, -5118321, 4456008297] ≥ 1 ℤ/7ℤ 11.17 42.16 2.53 57.96
#1752 [1, -1, 1, -360168, 989505963] ≥ 1 ℤ/7ℤ 12.41 47.49 2.64 54.95
#905 [1, -1, 1, -3, 3] ≥ 0 ℤ/7ℤ 3.26 7.42 -0.68 15.43
#1000 [1, 0, 0, -1, 137] ≥ 0 ℤ/7ℤ 5.16 15.91 0.00 23.36
#1014 [1, 0, 0, 159, 1737] ≥ 0 ℤ/7ℤ 5.55 21.16 0.45 28.43
#1015 [1, 0, 0, -141, 657] ≥ 0 ℤ/7ℤ 5.68 16.43 0.13 26.53
#1024 [1, -1, 1, 918, 5289] ≥ 0 ℤ/7ℤ 6.19 24.86 0.76 32.08
#1025 [1, 0, 0, 714, -82908] ≥ 0 ℤ/7ℤ 6.30 28.73 1.07 36.18
#1031 [1, 0, 0, -1661, 26097] ≥ 0 ℤ/7ℤ 6.52 22.12 0.67 33.87
#1035 [1, 0, 0, -101946, 12401892] ≥ 0 ℤ/7ℤ 6.64 34.78 1.71 46.21
#1036 [1, 0, 0, -5774401, 5346023177] ≥ 0 ℤ/7ℤ 6.75 44.71 2.64 58.32
#1042 [1, 0, 0, 2305, -15975] ≥ 0 ℤ/7ℤ 7.11 27.52 0.98 34.84
#1046 [1, -1, 1, -10422, 412869] ≥ 0 ℤ/7ℤ 7.65 26.32 1.08 39.37
#1056 [1, 0, 0, -1480, 94400] ≥ 0 ℤ/7ℤ 8.52 28.93 1.09 36.44
#1061 [1, 0, 0, -6800, 240000] ≥ 0 ℤ/7ℤ 8.81 29.22 1.17 38.30