curve #2955

y² + xy = x³ − 34417440789627547407397546862800802101555x + 2457624782485699185918829773125570732214412679464945519213025

a-invariants: [1, 0, 0, -34417440789627547407397546862800802101555, 2457624782485699185918829773125570732214412679464945519213025]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 18307122213101568954344266175402433870
discriminant (Δ): 4767212599777757543010186977076106578723060088734486134205495438837312845356723252956316145877942661041220384456704000
Faltings height: 21.8694
naive height: 291.6317
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 23, 29, 37, 41, 47, 97, 107, 757, 853, 2617, 97787, 300823
regulator: 93413263.7656408709031993613994845532823710569575340500
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:29:58 UTC
last updated: 2026-09-26 20:29:58 UTC

Witness: 8 independent points log in to add more points →

(50910570112336707648866270/452929, -29156994082994374365423422983802281975/304821217)
(42433066738459940211956/25, -8690749576983011914094952110460569/125)
(427781364384108126623/4, 20281327900229293774692970693/8)
(106882408849824018382, 3786590476454677500265829401)
(-91321154163838552114, 2199792621072654908554802578457)
(62765599966051461747045997730/533656201, 2358957744570844141668241033525918463219045/12327991899301)
(84660944818439003522530526/2627641, 5007588940901147337194534008292006521637/4259406061)
(131379669704137296634375892030/335146249, -43038515785458801609828093619450463282399965/6135522380443)

Commentary

2-isogenous image of D-z6old678-099, rational kernel x=-857545932178525503089/4. Source: https://dujella.github.io/tors/z6old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:29:58 UTC · history