curve #4634

y² + xy = x³ − x² − 33604035838218885070041259421030452838154x + 2324546212735498074282334111605326052053337046397188832666404

a-invariants: [1, -1, 0, -33604035838218885070041259421030452838154, 2324546212735498074282334111605326052053337046397188832666404]
c-invariants: [1612993720234506483361980452209461736231401, -2008407927803470336172678200685946429798954296052228573610731765]
rank (lower bound): ≥ 18
torsion subgroup: ℤ/2ℤ
conductor (N): 3300001758583385460319142337777169734770608439738303983614069920828533425042
discriminant (Δ): 94271977563329455643021956263521297181474913587622460441431943279657982767302864620186164388275951533563509169968197112592
Faltings height: 22.1919
naive height: 291.5600
primes of bad reduction: 2, 3, 7, 11, 19, 67, 89, 179, 191, 257, 373, 571, 601, 661, 823, 827, 967, 1289, 2939, 3089, 3719, 4799, 8011, 15907, 75659, 318348323
regulator: 23038579707792084315.168858073947283475132008165746439107530580557876077197
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-19 03:32:26 UTC
last updated: 2026-10-19 03:32:26 UTC

(-197949180262880264500, 1104545624958906803925326304602)
(-197854046199829987480, 1108152489485644190344356827522)
(-140699801955845832751, 2065737887318109663805467557993)
(-131953259639926956744, 2112151184456761713331174547734)
(-68811997818151757649, 2076313073476494755893934258324)
(-58687336264710984112, 2023498564027705643744061234410)
(11861222380319486123, 1388391158677350712375679909477)
(66380922283873050572, 621596331331514318061486322490)
(77840097378998368517, 424787272774921350419141241905)
(118473806414203926173, 79067024381589226063583432225)
(129713972241225682448, 384920143193484673604003178950)
(131475738187191169952, 423205952210053798495838662598)
(283966727838917271125, 3959844978952570223425865719898)
(314427799151159626035, 4779577126802283887904626497912)
(-118943958764900528015297531/608400, 565860632362864756212034834378261277243/474552000)
(1955264958040067995963/36, 175430079375201744423019690322615/216)
(4374569845336035977897/256, 5426705041931050517927558602952195/4096)
(3974767136458903768556/25, 125049372692661564911419818961714/125)

X660, T=6945/3056

last edited by Andrii Prokhorenkov at 2026-10-19 03:32:26 UTC · history