curve #4636

y² + xy = x³ − 178700526954669743047035136107399217392725x + 25854508894690297016610514025289552732695743708959036592375521

a-invariants: [1, 0, 0, -178700526954669743047035136107399217392725, 25854508894690297016610514025289552732695743708959036592375521]
c-invariants: [8577625293824147666257686533155162434850801, -22338295685012416622364350555790909782548509094340340359464726345]
rank (lower bound): ≥ 18
torsion subgroup: ℤ/2ℤ
conductor (N): 1034003231463690975784539963190598608272398539684971850419967708743459786
discriminant (Δ): 76449624461896644119900580111851398824736412374540433205995719591526596252993663948313291218555780638992352268686051139387392
Faltings height: 22.6934
naive height: 296.5732
primes of bad reduction: 2, 3, 7, 11, 17, 23, 37, 41, 43, 73, 101, 223, 227, 317, 359, 499, 619, 809, 1223, 1733, 3067, 3209, 9817, 10103, 11987, 20521, 70373, 230849
regulator: 44826109961988200158.437961458287504254778547316714573365361462781040820239
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:32:32 UTC
last updated: 2026-10-19 03:32:32 UTC

(-452562192315176469350, 3746625144216094795483212948511)
(44711729557021664770, 4237202404085694236105990477479)
(65042376817490320108, 3808748397989896140924817193239)
(108243875898772303558, 2789181998662594525440617662603)
(127611179691547404658, 2264602070392176401286776943703)
(168091194810974986642, 752251051650056184247932164599)
(375404879357481622674, 3416844610804773678103746382071)
(531757349886924451858, 9010661728918576687559051717239)
(691420340256154048954, 15259068796454691082357604772031)
(23913938072112004167826, 3697508627637670838421595273000183)
(61847549526936197953426, 15380612280356848500090842714550391)
(-1438184989326456675254518046/3031081, 10320000058678248449004809595425084361475/5277112021)
(2781673788786308738821/16, 13026455035409898566107639522279/64)
(16096782389198424271450/49, 553219318340541546170005760059177/343)
(16296293627285443668334/25, 1706362351000381538828348095957367/125)
(147350848290269913576466/1849, 276789278573254500252704552562784837/79507)
(459717412769909009570338/961, 210318413189028676157263769239770073/29791)
(685539937436043143072549698/5938969, 37644396420925340511136144634214178051867/14473267453)

X660, T=3559/1077

last edited by Andrii Prokhorenkov at 2026-10-19 03:32:32 UTC · history