curve #1963

y² + y = x³ + x² − 992808670120712069554428075750x + 390464313277187496260242213225523690822995304

a-invariants: [0, 1, 1, -992808670120712069554428075750, 390464313277187496260242213225523690822995304]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 157696982467068135411095164820700437213820173348774607927424665
discriminant (Δ): -3234577950607111621778307326923875456631208339563288061246794986834567975202750539673846875
Faltings height: 16.1454
naive height: 218.8750
primes of bad reduction: 3, 5, 7, 11, 19, 41, 47, 59, 101, 313, 821, 359509, 6773847828861830341411932979646390694497
regulator: 72715857537632735.41205432393617178454184001367438248738177142789902543034315
submitted by: Ritik Jain
submitted at: 2026-09-25 20:06:56 UTC
last updated: 2026-09-25 20:06:56 UTC

(942769584504349449/169, -901720110911304989069710556/2197)
(138703205822387085828452442156/30490396719721, -50512380137331502855560518965097397170275888/168362208001319334731)
(2125077179761536424341/625681, 94161845909723277100657693387712/494913671)
(688889594648183, -5783970083903684189006)
(-346033427871522, -26316830316481909586960)
(285763138241512506/841, 234374693476243883789505443/24389)
(138593817941502546198/2401, 1631366416528276575712528367776/117649)
(163394621914044357/196, 32717952178230951373167803/2744)
(684379573514088, -5617196451581073664505)
(149561120216212611, 57838690440792703204639222)
(-11096562574900524/25, 3408829899691156636992899/125)
(388342557702872529/169, 222348658216703926429635439/2197)
(838249145815613064/1849, -460515080217329190601531736/79507)
(-1008246494899804, -19144610612349663659873)
(1342950030035730141/676, 1390456103421459921545549687/17576)
(1603906611279660249/2704, -450530989734979424250161339/140608)
(513469800539345866735941/57851236, -365713606764932889457149008380798163/440016501016)
(-29470277104802851559259/27050401, 1882236746853778725983841121594112/140689135601)
(-104715191866069942480014/223233481, 91521745915790526699513237193605832/3335331439621)

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