curve #1990

y² + xy = x³ − 57504181461398316281504700528227568707875x + 5359523942861664681177505628843727425139054100914459850831361

a-invariants: [1, 0, 0, -57504181461398316281504700528227568707875, 5359523942861664681177505628843727425139054100914459850831361]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 45059046881492692973934369851657048339905118440376515737436574652340455125696895046568907070010708077314
discriminant (Δ): -239328073523887200927490570021656437165276525088303649123289308546184571546309258443184220461817195008038871571288321425408
Faltings height: 22.2963
naive height: 293.1911
primes of bad reduction: 2, 3, 11, 13, 17, 19, 29, 53, 52667, 2008536565073931521880979450174701677063857076066615910015272459713526406622844877149378549
regulator: 22135589767130352949646685249.3176477050721761910055757483383142980025375652033975160095473
submitted by: Ritik Jain
submitted at: 2026-09-25 23:06:21 UTC
last updated: 2026-09-25 23:06:21 UTC

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

(339169992089560117828770658929779640228471950/2184570296687501464515601, -1346969554733490393359890077994280208869818739284120959009619008031/3228858673645670425997000039507497849)
(1038423270950990889834420651488218403/7003635483051076, -178683086705825914380059428826547798473770766217396611/586118327309456092293176)
(-262651043507347554274, -1530988272233047231477111897447)
(2089377906432464258990, 94902006738458317705480032923561)
(466662690896565187106, 8952737013267467072360967959153)
(13477778830229452524626, 1564441080202292179276954288497821)
(156024306562375794339593/64, -61342043495375851229760253617900407/512)
(8136392797252288750, -2211828648754582330230635234519)
(115734107003749122539590/841, 5573491537547788588233160106320661/24389)
(70235320220785313918, -1291189448969733430458881848327)
(3514276301013692264114/25, -28997754902681103124032113058023/125)
(214272054610787077670, 1695804649084958873063549663009)
(5304731013116394320542/9, 358433466648988028363177315517011/27)
(128626042091279227694, 301765877129458289574093118505)
(128801833513707732416, -299484657642257508365772034369)
(-1966654292877593024114/9, -73898344854695848261916261634125/27)
(7115698663550343287005321786222/42579084409, 5672714767295369784262155912647620341378103099/8786066330543923)
(5626123856628045608074545235606560109461507168083987230/30543193522827740287037941265776969, 5383602837290261885297906652901902048563312681059282185610259010618382013246115827/5337915146775446028906286807021972244493885311670203)
(93982503070864278538624868605966277023841209432566950842678226472791036/1149408693246457589821591734855454552971192301094401, 42764069506743838466356958117593286170740323158814750383934722400195516955783961314203188119738334630677511/38968322988284455143816848388482414820080856076138455765249927986188743620351)
(128206652898228510376363502180734049716614200417331062/1534834152389466104380888016463001, 64172227544544999488108114004293098231708844105475509153811297992528299438401899/60130135363223259471445388987877403940198190413251)
(190018714525570935608148048503859692040217040519390/2958935687740950426803590666969, 7073811330340026596333211880932193372020938641354515195843007824405369038597/5089830136934013193747033993719239441389184797)
(42628770257137770459353995747454/658154145289, 737278253161138735737348784243583855165531511443/533938738986171163)
(-252285108545571522916794573098481177050362987701226451051263922214398448327589899467521108/950327620758113092012226127498573230377906934535963193376698175459641, 40552386414268954805845069810347442880339348033265648010259349750198893488540188146684592979014339780172960580893911843888300779535899/29296114744852016926402433784888349036915704322044465385785509312192180210324771803274991731612194257811)
(829805614172045361974367634622407419842186221899314034296475372963406162820643265967/5127588931864449873890267307459651193721497022739561029769432964, 198345155653213355852376957357580572452134859781256331212885086947308186700836963021265954610889310549550436912701021798839407/367172208826927861260241707883387010446748301872048031987640063354132078935764335899430212109688)
(2200804996054086483735458809571323243697481643717385575393283794/13457722933723509153530295383738174671665361, 28321903433646497812786495890900091898017319190330746389741011481790524275512277013215522075061/49369346016915035592032868062299300980281522176970673352504415641)
(797775437622541698528350241084242169718321188179256753783150085101256304224969801535486/7147584250732466350780792711856188815327258797596512327264009660841, 11005386636320746576433710157969934957515575129170893662050714724437910104866293895532200141633627620305291008612149562728491104611/19109042433857815548244071389057019366709592645949145679909641055336025657352683076066553274429765611)

Commentary

No commentary yet.