curve #1862

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y² + xy = x³ − 268409347762378385026812348079819316380x + 1732347721391983677030326921391021231913211799155496628496

a-invariants: [1, 0, 0, -268409347762378385026812348079819316380, 1732347721391983677030326921391021231913211799155496628496]
rank (lower bound): ≥ 23
torsion subgroup: trivial
conductor (N): 79045453030702383901499126432996625391697237140547605498568242436810804247757480750062
discriminant (Δ): -58865501782296146598364572557781461378406087942604480472250802290425283285888533525807485829513213961361523820269568
Faltings height: 20.9952
naive height: 277.1168
primes of bad reduction: 2, 3, 7, 11, 13, 17, 23, 29, 31, 37, 107, 9457353316542221997900392249170567479074584132753878098364089003848180967
regulator: 130211468270501208459414.704350408657685074295794110824575728281453277336551831840149
submitted by: Ritik Jain
submitted at: 2026-09-25 17:15:30 UTC
last updated: 2026-09-25 17:15:30 UTC

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

(-1654262421933845851815879938229323440/124634276787711601, 2392513108846334424466666948249002216898841321804610884/44000361737805472016027401)
(133618894914163928007530561164189832/14048688368828569, 10513356214470233945959598165841479733438728703714236/1665151176228347916919747)
(121192242553848550144/9, 638780234452002037318744842932/27)
(226134009455968382920/9, 2812505755623679575263461222748/27)
(19611436972518386396, 63333871574004325013052633236)
(233682418148616222056, 3563680125423023577415179535268)
(25310496614619905917/16, -2317920575312901599361831326909/64)
(890479404270606821225/64, 13462397672458965267625089909343/512)
(5909954683576603311920/841, 338984415133608748888634557753564/24389)
(12090352022803498208, 15953398307210861141469212324)
(230039541284677515224/25, 806679864770110085172040613908/125)
(9723883176090983300, -6465113842658248262640082264)
(-18852548193151818472, -9591772625447094879520903516)
(12772928232695070344, -19693861820337637066783811884)
(20053214925175694936, -66437228680319848295293744732)
(55494850631465390104, 397169115648082023804186944836)
(1945172176591103913421532/124609, -1613965234760898964063016953569279212/43986977)
(-55011896428527669903952199475940/10151813088481, 1779806190376533781676732840407128873034794878764/32345615496200365871)
(5970394434339609390761/256, 369946276529333368483403813513603/4096)
(-26191986056902719808153810/1515361, 64833884838192552050649014140923095456/1865409391)
(6438381616394868694725866299616/292519804201, 12742770127258520875016681464191049605636651916/158209628621915051)
(-40368032117505200873633253472063976/2160946987364169, 1514936776959340840778170824279496823075469112559308/100453753562299924399803)
(152688514171889602911215333312/20679302809, 36789467132552271036707231573656290890354156/2973745781842627)

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