curve #1873

y² + xy = x³ − 459334240227704871663368602680247943612755x + 119351879512113660662389987699121419743411439775392167059126177

a-invariants: [1, 0, 0, -459334240227704871663368602680247943612755, 119351879512113660662389987699121419743411439775392167059126177]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 295558366254516364346916340467636328003828052817136612424204168237528551339816960777327710
discriminant (Δ): 48710838495413345675837024785025189183859334284206861569182647082020776724875922346790085222271305069342892009329694720000000
Faltings height: 22.7765
naive height: 299.4054
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 29, 37, 83, 101, 103, 157, 2693, 39227, 4624231, 7290163846422251223951441721383273468447612492928083719447
regulator: 1180166983800757813997870.4499839297611458357633114607130950462841327672862599060233387
submitted by: Ritik Jain
submitted at: 2026-09-25 17:23:35 UTC
last updated: 2026-09-25 17:23:35 UTC

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

(664103386884404929294, 10353654849505748598348605768953)
(369316954613039956444, -291457671612103277772749114597)
(43887027375581319224039369689338367256930825651/82863792981743555041536004, -3744238234019210638632662757224792233938657710511116401861789203920849/754305393433148722738386463095913641992)
(3212299413008890597246/9, 25253995857587780965351576856131/27)
(539983768239132855134, -5363641158579255716624766826807)
(1437958038997050506894, -49316811428073351945388823562247)
(525547535065960364762, 4806895275009306714997935922385)
(-6552475648109040349987/16, -988958003622618303738422469961261/64)
(38787023245225488962078/121, 2990739083358885020530689360379291/1331)
(87672962797499298871910606/237169, -30041819123687818919505760994698305121/115501303)
(-85249053067177765413586/1681, 822778791391269909132048260813115313/68921)
(368646363464084287694, 345072630427596381422307404153)
(289522863080604396781118/169, 145074606664245667190717401502814701/2197)
(333341818616040151694, -1810092279195577156948975779847)
(2525330989460167468600286/38809, -72424798738202457675618233519176517291/7645373)
(1732233732231086755148272216219770686/2787174020578249, -1265268383104278657358109855942146223232731159736287459/147145209579983760183557)
(14870021455566041380414546789499438/29242364879641, 657101608762935440817674917624059730070866920476021/158131626412809144061)
(51584074599638139196516786169396/454323181225, 2537507303661179561352513796848269899845702029939/306229725456992875)
(20999149615668163859598828674/57320041, 214150839963773315931846642650491119153643/433970030411)
(52722787628105626036490392909365027206/196647784542317689, 343019753686998236257676366159172248244915161660022516779/87203433901135435058797363)
(194335252257792650675801777648351636426942006/573693318053531978086849, 704041909098332980456125999230257044474641887979620982240833251521/434529921764708337968868535790468257)
(-932946122250690677486134/9409, 11685142892839930384393457312269654289/912673)
(-58101259066814565496201153546155526/79399523030881, 5644009201100904743819194300462185007195767935113093/707500645299412504721)
(2823368240714576727388296812096005439/15005482179821956, 11565103581703500355780171418599744909721846481191613013/1838124539847038047989896)

Commentary

No commentary yet.