Elliptic Curve Rank Leaderboard

Curves with rank lower bound ≥ 3 and torsion ℤ/12ℤ

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 16 of 3920 curves
curve a-invariants rank torsion log N log |Δ| Faltings height naive height
#1105 [1, 0, 0, -4422329901784…, 98943710602886…] ≥ 4 ℤ/12ℤ 61.14 318.02 25.23 326.92
#1102 [1, -1, 1, -4240375358253…, 10627414422800…] ≥ 3 ℤ/12ℤ 36.39 172.19 13.40 188.64
#1104 [1, 0, 0, -2015047724010…, 34815737557101…] ≥ 3 ℤ/12ℤ 36.80 207.46 16.56 227.86
#1103 [1, 0, 0, 22560435880391…, 54047983322613…] ≥ 3 ℤ/12ℤ 36.87 184.45 14.05 191.89
#2139 [1, 0, 0, -1586501772830…, 29755509382256…] ≥ 3 ℤ/12ℤ 37.60 187.78 14.33 195.31
#2143 [1, -1, 1, -3014826139222…, 20148444419078…] ≥ 3 ℤ/12ℤ 37.95 178.05 14.74 208.34
#2137 [1, 0, 0, -2193596698337…, 12865671330093…] ≥ 3 ℤ/12ℤ 38.26 183.28 14.05 193.63
#2140 [1, 0, 0, -1819834111904…, 36464739063950…] ≥ 3 ℤ/12ℤ 38.43 191.75 14.69 200.32
#1493 [1, 0, 0, -1058306588646…, -1317017242620…] ≥ 3 ℤ/12ℤ 38.71 227.88 17.82 239.74
#1494 [1, 0, 0, -1210057483793…, 12237572864806…] ≥ 3 ℤ/12ℤ 39.07 218.03 16.88 226.33
#1490 [1, -1, 1, -9215871878203…, 31327842129454…] ≥ 3 ℤ/12ℤ 39.14 201.76 15.49 209.22
#2141 [1, 0, 0, -2744874623003…, 80881651709627…] ≥ 3 ℤ/12ℤ 40.09 189.80 14.50 197.31
#1492 [1, 0, 0, -9133867357763…, 58989289700011…] ≥ 3 ℤ/12ℤ 41.94 217.66 16.84 225.48
#2142 [1, 0, 0, -5447532560530…, 15475612753269…] ≥ 3 ℤ/12ℤ 42.20 192.85 15.57 217.02
#2145 [1, 0, 0, -1501450481401…, 70813267432828…] ≥ 3 ℤ/12ℤ 43.87 196.97 16.77 233.88
#1491 [1, 0, 0, -3531474678706…, 25483174836382…] ≥ 3 ℤ/12ℤ 44.08 209.82 16.36 222.63