curve #538

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y² = x³ + x² − 332879952815564345112147748595780x + 2604609520221493684125739925682176599698963849024

a-invariants: [0, 1, 0, -332879952815564345112147748595780, 2604609520221493684125739925682176599698963849024]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 3517040633993690361090388902476509267819430210749019327680451282814997562132496696
discriminant (Δ): -569972603079136088030749430753167865947695457931263752376725914885413249078218541703609138336579328
Faltings height: 17.6809
naive height: 236.4859
primes of bad reduction: 2, 3, 7, 13, 17, 31, 2309, 2473, 6958242341503, 76907118026079669077339391687619740585913716403158579907
regulator: 26986359629047678645971.99156785781321568480830235282974067659100643387754095762275
submitted by: wgxli
submitted at: 2026-09-02 22:34:11 UTC
last updated: 2026-09-02 22:34:11 UTC

Witness: 22 independent points log in to add more points →

(567419581434748717925971048184641834/36065379917336681025, -243292797536971167657420625238494451971965584685057098/216588686333569813701043401375)
(455400500419707766, -307077100614225175845560586)
(244406666058248386/25, 66691551357105608676238566/125)
(-3931690194167358, -1962807571112275142591154)
(17178137504214914458/5041, -439783753951688743255190616630/357911)
(3669880297307632579600282/6450820489, -805227440239079413865517701227504909230/518110549215013)
(21619718108107622145716148544/6259499689, 3178842384171910225565964120271529082549768/495232836894613)
(30104585015802670/9, -33381513826418834717748614/27)
(10137199932292972414257240655/508369, -1020650418584482822840348825044974821912746/362467097)
(-13799223148772371200680930/2057620321, -198772420093783615915782496263928481358/93335715380881)
(-513369901447641686/25, 110479270456095668186690862/125)
(-4551059906727408154279472/425060689, -19480377793705827231237183423722861712/8763476225113)
(-92304402210578731982/9409, -2025660325455706761311058001602/912673)
(-1376165294920304872304456009/555732975625, -765445559879558256798658773311022538426086/414285040004046875)
(-21150689980726565, -428314564431937238514732)
(7297656993157216750/49, 19573358405026332451179398226/343)
(9622717345346020062/1681, -64897561287996266286173179554/68921)
(182604817879968115124829679/17481335089, -1194766036764165137502753328618715694582/2311329681462313)
(168785154444176484923122311179662825630/16770599507039991012481, -1136460753738579412254676351898979379640575801107386072622/2171815267096248215668801373373121)
(32593287349101146900196555451198937015494/2286954730431316341455929, -3005536616015748896547908054418011020600084488074501615974338/3458488627625415169166389087874568467)
(4518678365251379756658666879567582707962/341907194210457105864841, -143280388226428344492015459570669697136075741588464392405774/199922815173623288051028610689108389)
(529221667046166856136896904157082/18385452699863089, -10240122556387418758628085147465458490226221768630/2492938081212596731295063)

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