curve #720

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y² + xy + y = x³ + x² − 300185418819609024349072268412778090x + 77900848309025657105485158009865508127600435621284471

a-invariants: [1, 1, 1, -300185418819609024349072268412778090, 77900848309025657105485158009865508127600435621284471]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 187951442378812057224317974598119745970432187010695375251448840427469548606306630118306
naive height: 257.0977 ★ record for rank ≥ 24
Faltings height: 19.4279 ★ record for rank ≥ 24
discriminant (Δ): -890404198352023219826003518752282790969843931127530506281688221910343678178716455911907704103114683496562688 ★ record for rank ≥ 24
primes of bad reduction: 2, 3, 7, 11, 13, 29, 101, 191, 2677, 3042761, 49068012959507, 139956448213282745397463385222339440926907375232362571
regulator: 7091878758050352628404442.2259421929683678004580988314240409284772839865757914304368188
submitted by: FNacc
submitted at: 2026-09-12 11:26:02 UTC
last updated: 2026-09-12 11:26:02 UTC

Witness: 24 independent points log in to add more points →

(38928279310712329471231313/60016009, 183688368772745409681983451472276084569/464944021723)
(-2732555788384092690659/4225, -10675854287913348319954976193381/274625)
(10067668374077446109609/25600, -588888805032815473805639897764197/4096000)
(4581221543793374146881/289, 309896473331076406653242169083507/4913)
(27445868832845103041/25, 129391754814822833195145002799/125)
(-142651795623458018568439/2839225, -1457825001331667052423360593543417889/4784094125)
(248001089925389777, -136776205537260756633177357)
(2735817071797608731, 4442229726000407724049773717)
(13561849935103525421, -49903441262381617604350477413)
(-1005426233226060719/9, -8956579095098920924775695463/27)
(465923828572143918761/2401, 19315993943250747926095374442443/117649)
(6894755145889600529/49, 67255897396171555536202752741/343)
(-34704141308299397919/169, 794830113984088251567490915207/2197)
(-1174414734697487279/9, -9150181604633814914854861927/27)
(153704236652199564857/289, -1287617465382523936458453130389/4913)
(13198990401068231369/25, -32253693917184607842292206513/125)
(-5770451440227878267/9, -2225584992586931199933712999/27)
(-283601993310726037631/441, -654145357954581299204615027201/9261)
(-14878033164229892179/400, -2386828005897920443840859818341/8000)
(10414055302323908305/9, 30545091202836359721767302489/27)
(13084474142121363389/49, 44435260565896393753919935533/343)
(-6490636922390711, 282575599501929790099284379)
(-118396344064853307, 334338242985333235890314299)
(-1186340250990481721895/1849, 6347510791077615588013635347929/79507)

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