curve #1947

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y² = x³ + x² − 24415973042781193267945662708366345x + 1450825294437138053187065745404498769050278280610459

a-invariants

[0, 1, 0, -24415973042781193267945662708366345, 1450825294437138053187065745404498769050278280610459]

rank (lower bound)

≥ 23

torsion subgroup

trivial

conductor (N)

523832720760204224204548552141118029432596158843283960416115025548270797255410232950879833096

discriminant (Δ)

22227012885053665936724361810204198861381409281078849100131190434836166151517275780969709604465156494592

Faltings height

18.6361

naive height

249.1552

primes of bad reduction

2, 3, 23, 29, 101, 439629499, 4885085939, 997438367837, 2653476831028242689479014521, 56999857438998409551342734921

regulator

9894428992975664853176228.23854557360273943606153119048802567739821817706868198841484

submitted by

Ritik Jain

submitted at

2026-09-25 20:01:20 UTC

later contributions

primes of bad reduction recorded · Daniel Błażewicz · 2026-09-25 20:03:41 UTC

Witness: 23 independent points log in to add more points →

(3211349433146408989294791/2307361, -5719989174033418842157217842835549814/3504881359)
(-144080174846949056574679428648226394374733163/910514571931468496332423801, 1010254768775386245423283583510588085045038729316200916327777113646/27474535010563183119883477779331526105549)
(36345505769635338597/361, 24886537931028224179195023294/6859)
(117264332469065115, -14149042332249263813149878)
(177793234017772815, -52248940526555050028495622)
(-45508227504404670579/841, -1246842699083637971174388145194/24389)
(-254845755923505190677/1681, 2814785978147522688911806793670/68921)
(109952773408115319, 9772806840956366423823882)
(3317942253178218783, -6037119037762292857278960090)
(-210567834954924528296841/1315609, 53534048979369635155146937038840558/1509003523)
(-51059407689360609, 50639661509259130328785446)
(-169825253593581601, 26446342911974574500740698)
(-1843207449765652923/121, 56770261517405387044255614174/1331)
(8700306167700099966/25, 23419546187699322153896825439/125)
(44676517203451515, -21193833760432208648586378)
(112282889573777119581/1369, 4060855145358700514741003994/50653)
(243118927821521543374988499/7370050801, 16514877123223752897091873650200684418198/632711491215049)
(-10565839608150396632450003148288331049417528203132743541933353527575093769745654601858086126626983299/66235641031103924351061185987019178549811855282352721560330558304713856707462369025, 611416814217361725255418911330662285146190784386655155158404775080459270310592812261804951641529197584435145335180156395752297457944723220610696798874/17046593922674134577887965153993886935907932382158248166885224806539607807347265105470018343136925824195356542439838732842625)
(-11316567443910904122934801/62805625, 268681260354739176880540774550258082/497734578125)
(245974426190032485140464265025156562664436412324954157049/3134718006608421350561498376602864272144, 746667764986662715075324515601683173937778544352733191198554792643527480671734590187/175508323561484964009360495594766264115919431691947118897728)
(3486183970895082438669874029287100957438114109/43884829413325377732834971001, 32564083071159271141530948270301195688495784422608857462933398125958/9193304008233021556283984740624920182168499)
(31772367701095785805536064854/495316141369, 4249237386919758183792586200717398933955363/348597061185664403)
(6170242668957262395514640679995308747528558232208089235468988652020895814/77515559039257711759428666606115647996149184513383840881, 2331598848327083259541648996241681326033741960035355352032063032758698662585925311289230792011857354752686103/682469622567079789470496948816281282778687202749214237770797398448653309453936788471)

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