curve #6411

y² + xy + y = x³ − 1684866795540631260893401708x + 23671613739990218790771761979832880497262

a-invariants: [1, 0, 1, -1684866795540631260893401708, 23671613739990218790771761979832880497262]
c-invariants: [80873606185950300522883281961, -20452274271351670345636081276026393074557525]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 532440708676887698875228747840243400833701980517875994525273047532906
discriminant (Δ): 64040247505531773061587570045464864915952258040414717268037464548516880838253225452
Faltings height: 14.6196
naive height: 199.6881
primes of bad reduction: 2, 3, 11, 13, 17, 47, 88420392947, 851902033184126233, 10310864753107410681110571441891893
regulator: 286898714981648162115.16634841833256942887905041452956527924572733356549457472898
submitted by: apkorte
submitted at: 2026-11-02 10:12:50 UTC
last updated: 2026-11-02 10:12:50 UTC

(836192490898, -149208999671284920529)
(29912437295089, 6116474530172226617)
(633032718353287/4, -15431307740427371280887/8)
(2475421321037728, -123144301445098289095915)
(-14159925358373501/529, -2709513684208268982531299/12167)
(-23968236331459139/1296, 10275562615169580479652115/46656)
(1925419365757201/64, 7458601229521670626459/512)
(-25887482488805, 223472098108462989611)
(16569146138179, -17425469228194183903)
(29875073341396, 441941071565660690)
(51469824059860, -270744793839071965159)
(66434875792231, 452718623018507151053)
(-43652756939729, 118480432626310807163)
(14910099273418, 43182888873119773031)
(37372570502044, 113588788770764921153)
(-45647503176641, 73933254337256886683)
(138410610626581/16, 6317471496334424835935/64)
(10879810280266219/361, -112159457036305233591877/6859)
(35459741498035, -92268717322406242309)
(89806443210976, 772441796056814630858)
(278197651584058, -4591923062226472321810)

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