curve #2001

y² + xy = x³ − 24023371105024673539326977391666146x + 516574761162917622756425912356565422955514306230340

a-invariants: [1, 0, 0, -24023371105024673539326977391666146, 516574761162917622756425912356565422955514306230340]
rank (lower bound): ≥ 16
torsion subgroup: ℤ/2ℤ
conductor (N): 2560824921463903740108076133817775448204077218700778327571510
discriminant (Δ): 772044197960812304179755970806263438291005699278201461045587943589221089384815336584499089904327067238400
Faltings height: 18.8187
naive height: 249.1066
primes of bad reduction: 2, 3, 5, 11, 17, 23, 29, 47, 53, 67, 73, 137, 193, 263, 311, 613, 647, 1091, 21589, 276047, 25155547
regulator: 6369735583990303847937.096208099724254553630310744663591163992498487894
submitted by: Steps Unbounded
submitted at: 2026-09-26 04:57:11 UTC
last updated: 2026-09-26 04:57:11 UTC

(158805928073574244, -26580048586403355043714994)
(1715267142129761687716/9025, -45497178341542205590166030676046/857375)
(20428492410370774836/49, 86068244033877075204600798930/343)
(183202722982611648964/1225, -702856280891433471188745933958/42875)
(37583174873860978084, 230402138639331336798191008846)
(138021400172916816676/625, -1208387786633815559503422345026/15625)
(154572790473475451464/961, 849861855326519745256303533490/29791)
(456541125375087866099956/297025, 306924588053975598395061271351716686/161878625)
(240635459354241847956244/1177225, -82252036455407633522213800709826298/1277289125)
(899746756961933342498836/4338889, -603040970877030887042649930996524918/9037905787)
(345437225998875302992706596/2392481569, -890753485352112984554601863193332813138/117023450984497)
(808801735032541327653844/5480281, -174800239627932579757749051424241594/12829337821)
(120691859739022686948264/844561, 1067621238178226516622995396307810/776151559)
(1084778031219288981730620676/2429011225, -33617732908694630706917790274513353912554/119713818224125)
(130987059836752631747251396/12866569, 1498967987259274493232456871778805575738/46152383003)
(94242549257461207189962484/560789761, -464899340911769896575409648476068430850/13280062330241)

2-isogenous partner of curve#1100 (Dujella (2009)).

last edited by Steps Unbounded at 2026-09-26 21:36:35 UTC · history