curve #1957

y² + xy + y = x³ − x² − 4504429865794006964703312317x + 112022925101216863066000946768065071730309

a-invariants: [1, -1, 1, -4504429865794006964703312317, 112022925101216863066000946768065071730309]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 33085862110607740794252002782317079038402111628025703810
discriminant (Δ): 428013635420429134500583623252881354580550020567374503390905783788591268249600000000
Faltings height: 14.8118
naive height: 202.6382
primes of bad reduction: 2, 3, 5, 7, 13, 29, 47, 83, 101, 353560086666418284426445401681935332479095131
regulator: 1496705127009023.3349168248926252084316744004397737934282457688329851894745
submitted by: Ritik Jain
submitted at: 2026-09-25 20:06:39 UTC
last updated: 2026-09-25 20:06:39 UTC

(3342260263125365766583/22024249, -176718674129222033848484133110488/103359800557)
(48748773346927, 91028383051373020616)
(398371198202959440744489893457820513/2357951522516988888064, 233908173459491256899071484609676538679429869791533567/114499162007224788729491454656512)
(45572023155823, 37300703927151952328)
(-382872087247769/9, -12854312103281852425064/27)
(29040175249967, -75524812039156340984)
(24603247006110403/484, 1277844306017868644817743/10648)
(734778814335502783/3249, -604657920171294890068369912/185193)
(-3758935616762081/81, -342799159964752462615928/729)
(99402788764364503/2209, -2195089467866208937014632/103823)
(23652016973756143/529, -28920043918051146285128/12167)
(-71363172886033, 264654390213614995016)
(-240936656891739737/4489, 134225863132076668800445208/300763)
(3705268610633119/81, -29989533573696694698872/729)
(13207083033145967, -1517765815874418458236984)
(56021255648361703/9, -13258796819322582395502568/27)
(393891954784025252351167/8506557361, 40988383611925604074016059249680376/784568291962391)
(-4644574839106533907726577/93460438369, 13190965876744252974298198386329300552/28572070995102097)

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