curve #281

y² + xy = x³ − 26209631133105489807468060702x + 1629345706371694346940183718532493403517124

a-invariants: [1, 0, 0, -26209631133105489807468060702, 1629345706371694346940183718532493403517124]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 1213665079954461658249582950514846025457164454739340273989176554979798
naive height: 207.9214
Faltings height: 15.1326
discriminant (Δ): 5432877975727185226735785866014954478423233775179229622774668572659776350389518843904
primes of bad reduction: 2, 3, 11, 23, 79, 463, 61651, 6857983864531, 743660058281821, 69519711615691712465655885193
regulator: 6322033340983346351.110600296802321528004633108249976629120584642841804475837
submitted by: 7fff-zip
submitted at: 2026-08-22 05:30:32 UTC
last updated: 2026-08-22 05:30:32 UTC

(598407572689908254468956/4457565225, 216697675239612511809503774832794234/297609342247125)
(40781714677404, 792652517094426533970)
(78918141773420736/625, 9017907587884486381093566/15625)
(5571677317885224247140/51251281, 93431099745980861393595377853222/366907920679)
(12935886659458152/121, 295270509389663093894166/1331)
(399589923185032553100019428/3782818832809, 1460964809737039001571569276696613767718/7357382140415366123)
(105087930519012, 188588253118526316402)
(100446054426924, 100663160477077925250)
(280324522020535252575/2829124, 342012409117100110519292197101/4758586568)
(98594547288540, 60375623535434832018)
(47440755557023911/484, 481052075997234437051523/10648)
(16239955611376374673308/165817129, 91493267843862874357454147996058/2135227170133)
(15562093386012958126428/159542161, 59234172541333629645476456211390/2015177035591)
(3544550064535630308/36481, -29534354078219911060517418/6967871)
(35081577952414692/361, -50721660131539536334362/6859)
(186005551132850585523/1844164, -272876243756841744179150086431/2504374712)
(101327498955852, -118090351735566883374)
(101403219801428, -119560848746931183310)
(104386031988288, -175678253601128085810)

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