curve #4127

y² + xy + y = x³ + x² − 18613248623774455314096168491709628926683827040x + 329573422683661309929628277175805475478025888414614329402376260154497

a-invariants: [1, 1, 1, -18613248623774455314096168491709628926683827040, 329573422683661309929628277175805475478025888414614329402376260154497]
c-invariants: [893435933941173855076616087602062188480823697921, -284751437198683371779205532249400489616927442210883796070066694951219969]
rank (lower bound): ≥ 20
torsion subgroup: ℤ/2ℤ
conductor (N): 368471581383911304150906411175917477107662947926231328206990677277830533511360110
discriminant (Δ): 365788188926718968184902472361718649194749616248079683716874967453007132750554660809964112519666301589327994951420764695507133477596521600000
Faltings height: 25.6638
naive height: 331.2342
primes of bad reduction: 2, 3, 5, 11, 17, 23, 29, 31, 41, 83, 151, 191, 193, 197, 199, 313, 431, 461, 509, 977, 5939, 19001, 174673, 1267939, 1912969, 4462121, 710126761
regulator: 506208374089058775076102.276038783249343400509524740144672460439000573182308522
submitted by: wgxli
submitted at: 2026-10-10 00:57:17 UTC
last updated: 2026-10-10 00:57:17 UTC

(4424159569129268667357, 15726157686436108324799083783437421)
(-29610671407234919325483, 29236309887024503026407578249308501)
(-62958750729984107209009, 35381974741521412445583789256973119)
(-78356080620677689626259, 36151815088164352671849080126353589)
(-97702146972264959483023, 34863899101917208502577667043232581)
(130313131024408756042387, 10813728752274863083913946115192001)
(144384933121773535299917, 25536146001092145569602607525640701)
(201051304881346617654557, 68659860119716634022548038036228021)
(-100555389161880342695043, 34416296987199299996432075167799221)
(242778098272908928052857, 100599791148676685011924628651956421)
(674805890636403723066657, 543185853702290351235935692427863321)
(813696601304895589993685, 723833069673104957645212696054187093)
(4151378741943788420699325, 8453856738039999051208430533608533941)
(1238688649424675249548333/9, 522783720359835776612735836157936327/27)
(2301636253036688630040913/9, 2993848641024445276994756700134916167/27)
(-830728128730728802989327/49, 8679070865454766491807783603880357363/343)
(-8032068802872878015276295/64, 13437917343841081397716268453380378961/512)
(127614468252548974481585033/169, 1418452903837029498467494451462781196237/2197)
(-130307971384037316397344027/1369, 1782873134519584357845859323355867436353/50653)
(-57672839417845875403013142819/442225, 6826877581384622752227725350112704727743709/294079625)

2-isogenous to curve #4126

last edited by wgxli at 2026-10-10 00:57:17 UTC · history