curve #623

y² = x³ + x² − 92246609709815389969020059372465205225x + 331132209438234089164008892190536770183562030214546807739

a-invariants: [0, 1, 0, -92246609709815389969020059372465205225, 331132209438234089164008892190536770183562030214546807739]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 104248168115693608073559801519130263017579290095801453847349400259924673492465624274936
discriminant (Δ): 2869700364901611096507954920543957666840667831268238033728898950778417853554939947629267420286762879862265391871232
Faltings height: 20.7355
naive height: 273.8662
primes of bad reduction: 2, 3, 7, 17, 19, 41, 43, 59, 107, 176201, 3503531, 386420005781, 207451676650029946400131, 3488009355806088776834671631
regulator: 1244279570167775793247358.7249947723513185787348810796712546812863101408532467411609094
submitted by: wgxli
submitted at: 2026-09-07 07:15:57 UTC
last updated: 2026-09-07 07:15:57 UTC

Witness: 24 independent points log in to add more points →

(-60801552592356814523/9, -686243509657126292355344304850/27)
(114682587802675834103, -1223956065513446786120761661430)
(-62973405767859595668525969/14055001, 1348032444650441584155572196607456533246/52692198749)
(59556332728263957171534/7921, 5577862364532122233156186964517747/704969)
(-10339873162296683970, 13397157600701250853685058333)
(-1613290598145360834633/361, -175425004991092841964263329712226/6859)
(26613475708652338838679/4225, 1653861316220802049158545565258/274625)
(16972581516908828625261600507/2555201401, -437335028151419842509523417925856666046866/129162875619149)
(4603551931825611160461949509453081/1117468623673600, -171290525320865898496610652478581758318809109986179/37355366934590358016000)
(4512189901810429455, -2601063819039519480695254458)
(-10628131741199953360425/3721, -5425322143164839394723813913057602/226981)
(-50357560765382494083637384364506256301/8780488285218254641, 674239119954189267486892404943281699628243283964063114378/26018245168704605958255300311)
(6881781962988507429, -4714333100533612256596441938)
(347869888421318137097649819/74425129, 925687772691731983755947198356041100482/642065587883)
(330346959317279805704064016779/51907875889, -15967265517341479356991547785423199353183302/11826327087418537)
(171773144242303119657130727180451/58035676153225, 4052860597095326649447221040686514721249843941774/442122455038025670875)
(5621437848520049579842123618834446/772795242648025, -144139039883123240809065591001747613454082607996919/21483085645444763339875)
(11312590395358253780810637247255352019/1781853950724606529, 2793091655260218704739268599009688685661444925355855718/2378527387500839862573419167)
(63713870435796890810281130851782/10071502114969, -27496060799143374809703417863310520209721887045/31962546466487364547)
(73241747219463270603579/11449, -2054579854202496673441964289224622/1225043)
(7899609984299295437677980756099620127915/651560358504557419129, -524593911783356065674262086724466477982439612874833889047986/16631521454904624944512650055117)
(513183708827619155708761907291607597/81458150580840049, 3653773609795278842121444004413899502291820023005850/23248868364382278269148407)
(23904401262749779380298866447383101749687/3744298257448939940929, -356355387475548559943440845581117765191033094145735062060490/229116124021816913409949234042783)
(28797967152953632383948421101/4571788225, -5898013830850768998206712298198590044826/309121460833375)

Commentary

Specialization at T = 37/273 of the rank-16 fibration of X948 given by: y^2 + (Lx+B)y = x(x+D)(x+E), where B = pE + qD + pq(L-p-q), L = 1550575T^2 + 383162T + 660881, p = 1455298T^2 - 3980701T + 45675, q = 2797961T + 2191222, D = 13(21450365118T^4 + 101744274573T^3 - 254054389162T^2 - 704051116967T - 25228006650), E = 13(37097177040T^3 - 433829517136T^2 - 468269695247T - 77172736410).

last edited by wgxli at 2026-09-17 17:34:45 UTC · history