curve #4606

y² + xy = x³ − 6899304545006938220091703682504249831562979781407325x + 223509511711375852266654850860978612180001050075694625084363340161710630280625

a-invariants: [1, 0, 0, -6899304545006938220091703682504249831562979781407325, 223509511711375852266654850860978612180001050075694625084363340161710630280625]
c-invariants: [331166618160333034564401776760203991915023029507551601, -193112218118628736358389791640635448164020459112002821213195913772252528823787401]
rank (lower bound): ≥ 30
torsion subgroup: trivial
conductor (N): 1392541353498585911918735590900669541332261058878763384246047140988328330518488331721054740107957202682513906649146966203871730
discriminant (Δ): -562989385415761632416576048827163043817470684283318778148766317844511420489932797015265241314364981144804183759243108933439900159538189077775301184480000000
Faltings height: 28.6878
naive height: 369.7298
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 29, 41, 421, 1976338341221281008229, 1277419544474836978017581, 1931258306751832495845149262697066400101431014547456098129486380190669
regulator: 15829438062037750459243354141713392.749582898245448777428841556568478462682182390944841476062630141
submitted by: wgxli
submitted at: 2026-10-19 01:15:58 UTC
last updated: 2026-10-19 01:15:58 UTC

Witness: 30 independent points log in to add more points →

(336813932928449488459060, 470303910277699500496333107916755829165)
(1366254067996477350122350, 462694131288492308836308937162901749975)
(41735680229712235982287900, 90886455014351873305670954435702568175)
(42159212386540081197431530, 87028822731147890468153078610586583575)
(43023843105327116974561450, 79462233077176019272367772156943785175)
(44089596854298778055526850, 70904122861169863150446116776156140175)
(44206195918655417183645650, 70033635965623961349849326989053564175)
(46206781933362777162585130, 58046639636465635824688724388861704575)
(46306065662350132482182650, 57634392818605384995735646342022547175)
(49619511582479790832456312, 57770125752586885015373738026320103927)
(50299581186292655053163206, 61136983391303016476823545065385489287)
(52850422170537684778587010, 80612750232122352635544225705888587215)
(53009787184758252970300930, 82087379633304980734859640600647462575)
(54115296098959744247341570, 92878246563040777141461025781200555855)
(-1671006945337593990291470, 484802672879587240816423199668991978575)
(12510413187459765583788610, 373034008364195852953253807947919833615)
(24344560556642145716289220, 264531593477750269811445656020970288575)
(36135667227965340296108290, 146232701720322770418861078893225373775)
(59263414577191999490411650, 150914891296152687020245343878847700175)
(59271529096855353752046400, 151012681145064439902920663651895026425)
(60373537798234047401549362, 164418562851971813962950511323898837711)
(65193912508120107433017970, 225404160500849590966938026420652938575)
(75895242871828781044207930, 370200468718663786735252784441311534495)
(112862747209903512231323650, 939404432553678162889381048461286080175)
(167358492830802184526637850, 1938136670696149270415736359307642615175)
(188737608291957057880870150, 2375824195926239028410371028151048082675)
(216489157712104396183279042, 2979295634210756410612402870748040963727)
(2238643554593436105536946352, 105847987634973656643768693397791995189671)
(4093193471161553815008571600, 261821121380988784447991443241535684031975)
(2587136677256000025569874850/49, 27487746490144853851191630611404419420025/343)

Commentary

specialization at T = 16425/13472 of the rank-16 fibration of X1152 given by: y^2 + (Lx+B)y = x(x+D)(x+E), where B = pE + qD + pq(L-p-q), L = 242986T^2 - 880768T + 331027, p = 150843T^2 - 960535T + 684442, q = 68393T - 24870, D = -8941698528T^4 + 80955405956T^3 - 84314868357T^2 - 53869522151T - 63795270, E = 12246629473T^3 - 17749365633T^2 + 4456572374T - 7530096720.

last edited by wgxli at 2026-10-19 01:15:58 UTC · history