curve #3829

y² + xy + y = x³ − x² − 85710829754668076704037373698240228217x + 304282234011154392147046942976973309638777108889737609241

a-invariants: [1, -1, 1, -85710829754668076704037373698240228217, 304282234011154392147046942976973309638777108889737609241]
rank (lower bound): ≥ 25
torsion subgroup: trivial
conductor (N): 26083033039158138808547307384350963590889216846305036787438239201805477742984111231459014859070
discriminant (Δ): 300455306844086827741888294446390531676208007469817122463579572862126305267283781340942670110696871380669696000000
Faltings height: 20.6278
naive height: 273.6457
primes of bad reduction: 2, 5, 7, 13, 17, 37, 41, 43, 8635477, 2383478558073859, 6415537888871913097459, 195741578443980823165620502694226568055923
regulator: 148902692426786471015896232.9366683606745607116980217895364497912092667721378764728375203
submitted by: 7fff-zip
submitted at: 2026-10-03 05:22:13 UTC
last updated: 2026-10-03 05:22:13 UTC

(5622175987724264871, -333848348126245360387891636)
(7295269170958162751, 8201209204643771867961050644)
(9319164806754644471, -17744543747379467404720864436)
(7242518409705453231, -7963639897049303459174697876)
(5825401733244612421, 1633708791837484776483707914)
(5047641179724093671, 501958195823998290142017164)
(2091859017181111463631/361, -10150739288403094413901285276524/6859)
(4466232874162644711, 3250647632653848018352248204)
(63680109356205565671, -503069583311792548165185182836)
(1323250947989211871, 13899003579701252260921342764)
(126559498436450802639/25, 43039939872986557110934577628/125)
(5006145200770631911, 814144777621094902720236684)
(5695210817590760571, 931439581129549262251016364)
(72071172286760641351, -607027979759323602590848496756)
(6322445319002433271, 3887067883776327089358034764)
(2269239628166751289/9, 453959318217819875850411511178/27)
(5825432907603891799, 1633862352682567432341848284)
(6159956123771200471, -3169729438926126689769104036)
(3703114282654892371, 6137283390943569191461759264)
(25949380392011991271, -124714403660569979120586597236)
(4987805101981980271, -927864019392278678716227036)
(8602479930229463271, 14267548728724510449565914764)
(4865328293099315671, -1562093317059583539484182836)
(-9029561542880993849, -18493414242962282235276259956)
(6003227634828465671, -2467667795924763142421822836)

X1008; T=-127/460; 2-neighbor step: yes (Q has vector q=[0,0,0,3,0,2,2,0,3,-2,-2,2,-1,-2,1,1,0] in source section basis; h(Q)=12; F'=O+Q-F).

last edited by 7fff-zip at 2026-10-03 05:22:13 UTC · history