curve #1902

y² + xy + y = x³ + x² − 4713277155979338448440943324774775864953788x + 3935089641489957086593050469170343495099921096768724427886097181

a-invariants: [1, 1, 1, -4713277155979338448440943324774775864953788, 3935089641489957086593050469170343495099921096768724427886097181]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 2798758120787777099654612256602983581376873284311485831319951631008617690053822368963890906898832624022950
discriminant (Δ): 11653393374406062132513376653785949822278095776332301814787410087511879584824520296979260702151222188687918701174008964782080000
Faltings height: 23.3009
naive height: 306.3905
primes of bad reduction: 2, 3, 5, 7, 17, 23, 101, 487, 709, 195480184419659168045163233416466328467861329417667422814429989725349527629561964384865762343
regulator: 52940635892626584651877164930.2908987640954351806660175906156197662547917812195739978241987
submitted by: Ritik Jain
submitted at: 2026-09-25 17:48:26 UTC
last updated: 2026-09-25 17:48:26 UTC

Witness: 26 independent points log in to add more points →

(82874201102528221341630092487727645/64564551532849, -74404630352006707369060208719145245685609322063169/518789536428609014743)
(-2007333333716069431175, 72855232634398945454694866629757)
(11719133295034889964529/9, -63924114391884627039949572057569/27)
(11886890824135723470085/9, 100763193336359299098225464040419/27)
(1174728339765642722125, 4402141021718033540921766093017)
(8225670443159132521669084552239000295365442320136195509/177232615946521111004203542249481, -23566216514729811508944868550846483369946781380078841422718606129082297880159445987/2359475496812245743836599648312540369542589382629)
(22280803447677270828285, 3310569795855841677779334209231577)
(11075528109706249731725, 1144700152449883876656949488756057)
(181635106189757322048451/9, -76979901781507436064300325883012681/27)
(2385611853110552359365, 79170071171409295495619421384537)
(1283541426195744336021, 100902067328222944492625033105)
(1286518633368288066301, 852403266487468933001507830313)
(2622903447447941524538029/2209, -369932119829799844172507176570988105/103823)
(237444581279410972635, -53191490197434024032513682143473)
(-45862751200486547030219/169, -158339239264895721115298340824393011/2197)
(-44639384803474711482022059/55225, -1102491706664655197037750414598666904869/12977875)
(12192417828430999231998964761125/1274561401, 41560292888450698318626261820274416408633131717/45503116577101)
(-4913778308885566608172554493075819149/35065036490639236, 444991156184468932286611103215028668448376899732594212303/6566159722503254103793016)
(2019288911749539037234335/1681, 178049843740552304158697086771697917/68921)
(2458918682131997685495849195/1697809, 26799075958143935026296107110252996827209/2212245127)
(134045305169814225105410011/168921, 1829776767919446035713884034219001180773/69426531)
(-1698293518736378836742490930075516171/1453590427212361, 4909246255207213074480846348619794003968147689973895677/55419561009680358451141)
(-67689503174649700035598299109672931/38941106958961, 20149931520551289067290876988638746451307524201760033/243003449874972108041)
(81499039808598781666398175/77284, 251893947961778516106043586990941099789/21484952)
(1404032519226186092412030657288577415317195069181505/1193420661273047278823818272361, 5590410836641385906243134722729287959665940346426755775574153022336589106753/1303738013409227155923664493523304645663165109)
(16275778601749965925965258348825035866109731387042948145725/43956737415714785607599147637590296249, 13795192374113304425396024121093643425847031041674745059848784606541528906543465864409819/291432630100778659728083197286635393642193871079958388307)

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