curve #304

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y² + xy = x³ − 1998675662524543869448537818094316x + 34278416330918655840201783804131603181718906590096

a-invariants: [1, 0, 0, -1998675662524543869448537818094316, 34278416330918655840201783804131603181718906590096]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 5006405484397324349874708489421058031687284832245658288472672302438681604464636090
naive height: 241.6470
Faltings height: 17.9564
discriminant (Δ): 3379337256877848416704903412257177388986372653464337778640355908107748274947815216082189778984960000 ★ record for rank ≥ 22
primes of bad reduction: 2, 3, 5, 7, 17, 19, 23, 154313, 9927928313985692559851033, 2094668112397900418825126769126151468330160369
regulator: 50421388073501899175643.80528277641215771397332774788377869211586893221721618586416
submitted by: 7fff-zip
submitted at: 2026-08-23 23:45:57 UTC
last updated: 2026-08-23 23:45:57 UTC

Witness: 22 independent points

(30687178017973540, -1357536329681179128849704)
(441754341631668276400504/52171729, 1597096133788197267650086044201831404/376836398567)
(271426736228615776984/9409, 723211777746903464703446584276/912673)
(1664822541458426262532984/10582009, 2069370525165457806980342602441569124/34423275277)
(1100501148781529189464/33489, 12387188161059024818833730493644/6128487)
(2525435083338394200061816/403225, -4013222884187939797516949012579646244/256047875)
(1278269573160564376/25, -1013646601193310951926357116/125)
(4522678477939161876536200/166229449, -427216352867874813283949727794638348/2143196285957)
(96661078737955679770/3481, -89545215601274543471026863136/205379)
(-9859980225011231068979264/281601961, 37008655296136822523187817527802003292/4725562507541)
(-61132210869984279179/1296, -226666886534001164805054257953/46656)
(3890776558930992489123148/188485441, -3488063601593422601119069108983213500/2587716619489)
(-9437412423852680, -7231887857434329009488684)
(-15663433173402407372/361, 43006832744785274329964226808/6859)
(1289747417719901426417560/57168721, 353843834975313293626718204700967156/432252699481)
(10597504636337899249/1024, -125644270685532172983046210759/32768)
(45261372472589404777240/1885129, 938882948291280528349337862090788/2588282117)
(106448763511876225510/4489, 140335648607927089344582300382/300763)
(21324767605240764599116/942841, -734313816226661326619631317612368/915498611)
(-108206584900585908422840/2486929, -24451538852365271272085850691942732/3921887033)
(22791878369398768, -751355051716591634383148)
(126146254602418084/25, 616465083410559845129237492/125)

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